Road surface frictional coefficient estimating apparatus

ABSTRACT

A road surface frictional coefficient estimating apparatus includes a device which determines a first estimated value of a to-be-compared external force acting on a vehicle due to the resultant force of road surface reaction forces by using a determined frictional coefficient estimated value and the like, and a device which determines a second estimated value of the to-be-compared external force from the observed value of motional state amounts of the vehicle that define an inertial force corresponding to the to-be-compared external force. The estimated value of a road surface frictional coefficient is updated on the basis of the difference between the first estimated value and the second estimated value. In the case where the first estimated value and the second estimated value have polarities that are opposite from each other, the updating of the estimated value of the road surface frictional coefficient on the basis of the difference is not carried out.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a road surface frictional coefficientestimating apparatus which estimates the frictional coefficient of aroad surface on which a vehicle is traveling.

2. Description of the Related Art

As techniques for estimating the frictional coefficient (hereinafterreferred to simply as “μ” in some cases) of a road surface on which avehicle is traveling, the techniques disclosed in, for example, PatentPublication No. 3669668 (hereinafter referred to as “patent document 1”)and Japanese Patent Application Laid-Open No. 2003-118554 (hereinafterreferred to as “patent document 2”) have been proposed by the presentapplicant.

According to the technique disclosed in patent document 1, a roadsurface reaction force acting on each wheel from a road surface (acornering force (a lateral force of a vehicle) and a braking/drivingforce (a longitudinal force of the vehicle)) is estimated using a tirecharacteristic set on the basis of an estimated value of μ. Then, basedon the estimated value of the road surface reaction force, the estimatedvalue of a lateral acceleration of the vehicle and the estimated valueof a yaw rate change velocity of the vehicle (the yaw rate changevelocity at the center of gravity of the vehicle), which are motionalstate amounts of the vehicle and which occur due to the resultant forceof the road surface reaction forces, are calculated. Further, accordingto the technique disclosed in patent document 1, a previous estimatedvalue of μ is updated on the basis of the difference between the valueof the lateral acceleration detected by an acceleration sensor and theestimated value of the lateral acceleration or the difference betweenthe differential value of the yaw rate values detected by the yaw ratesensor (the detected value of the yaw rate change velocity) and theestimated value of the yaw rate change velocity, whichever difference isgreater, thereby determining a new estimated value of μ.

According to the technique disclosed in patent document 2, a tire modelset on the basis of the estimated value of μ is used to estimate theroad surface reaction force acting on each wheel from a road surface(the cornering force and the braking/driving force). Then, based on theestimated value of the road surface reaction force, the estimated valueof a lateral acceleration of the vehicle and the estimated value of thelongitudinal acceleration of the vehicle indicative of the motionalstate amounts of the vehicle generated by the resultant force of theroad surface reaction forces are calculated. According to the techniquedisclosed in patent document 2, in the case where a slip angle (sideslip angle) of a rear wheel is small, the estimated value of μ issequentially updated by incrementing or decrementing the estimated valueof μ by a predetermined value according to a magnitude relationshipbetween the estimated value of the longitudinal acceleration of thevehicle and the detected value of the longitudinal acceleration providedby the sensor. In the case where the slip angle of a rear wheel islarge, the estimated value of μ is updated by incrementing ordecrementing the estimated value of μ by a predetermined value accordingto the magnitude relationship between the estimated value of the lateralacceleration of the vehicle and the detected value of the lateralacceleration provided by the sensor. The road surface reaction forceacting on a wheel depends not only on μ but also on the slip rate or theside slip angle (slip angle) of a wheel. For this reason, according tothe techniques disclosed in patent documents 1 and 2, the slip rate of awheel is estimated and the side slip angle of a vehicle or the side slipangle of a wheel is also estimated using a motional model of thevehicle.

Meanwhile, the direction of the actual lateral acceleration orlongitudinal acceleration of the vehicle or the direction of the yawrate change velocity naturally is not always fixed to a certaindirection. Hence, the estimated value of each of the lateralacceleration, the longitudinal acceleration, and the yaw rate changevelocity (the estimated value of μ and the value obtained by using amodel, such as a wheel friction characteristic model) or the detectedvalue thereof (the value obtained by a sensor) will have positive ornegative polarity indicative of the direction of each of the lateralacceleration, the longitudinal acceleration, and the yaw rate changevelocity.

On the other hand, for example, the estimated value and the detectedvalue of the lateral acceleration carry a meaning as the observed valuesobtained by observing the same object, namely, the lateral acceleration,of an actual vehicle in different ways, so that these two values shouldbasically share the same polarity. This applies also to the relationshipbetween the estimated value and the detected value of the longitudinalvelocity and the relationship between the estimated value and detectedvalue of a yaw rate change velocity.

Meanwhile, there are cases where, for example, if the absolute value ofan actual lateral acceleration, an actual longitudinal acceleration, oran actual yaw rate change velocity of a vehicle is relatively small, theestimated value and the detected value develop polarities that areopposite to each other due to an error component included in theestimated value or the detected value. In such a case, it is highlylikely that the difference between the estimated value and the detectedvalue contains relatively many unwanted components that are notdependant upon an error of an estimated value of μ used to determine theestimated value.

According to the technique disclosed in patent document 1 describedabove, the polarities of the lateral acceleration and the yaw ratechange velocity used for estimating μ are not taken into account.Similarly, the technique disclosed in patent document 2 described abovedoes not consider the polarities of the lateral acceleration and thelongitudinal acceleration of the vehicle used for estimating μ.

Hence, according to the aforesaid techniques disclosed in patentdocuments 1 and 2, in the situation wherein the estimated value and thedetected value of each of the lateral acceleration, the longitudinalacceleration and the yaw rate change velocity of the vehicle havepolarities that are opposite to each other due to the influence of errorcomponents contained therein, the estimated value of μ may beinconveniently subjected to improper updating based on the difference.In other words, there is an inconvenient case where the estimated valueof μ is improperly updated on the basis of the difference in thesituation wherein it is highly likely that the dependency of thedifference between the estimated value and the detected value upon anerror of an estimated value of μ is low. Inconveniently, therefore,according to the techniques disclosed in patent documents 1 and 2, theestimated value of μ develops unstable changes, i.e., the estimatedvalue diverges, or the accuracy of the estimated value deteriorates.

Further, the difference between the estimated value and the detectedvalue of the lateral acceleration and the difference between theestimated value and the detected value of the yaw rate change velocityare also susceptible to an estimation error or the like of a side slipmotional state amount of the vehicle in addition to an error of anestimated value of μ. For this reason, even if the estimated value of μis updated on the basis of the aforesaid difference on the lateralacceleration or the aforesaid difference on the yaw rate changevelocity, the error of the estimated value of μ may not be properlyreflected. In such a case, it is difficult to determine the estimatedvalue of μ accurately and stably. In addition, according to a finding ofthe present inventor, the change rate of the lateral acceleration, thelongitudinal acceleration or the yaw rate change velocity relative to achange in the μ of a road surface, i.e., the sensitivity of the lateralacceleration, the longitudinal acceleration or the yaw rate changevelocity in response to a change in the μ, changes according to abehavior state or the like of the vehicle. In a situation wherein thesensitivity is low (in a situation wherein the sensitivity is close tozero), the dependency of the difference between the estimated value andthe detected value of each of the lateral acceleration, the longitudinalacceleration or the yaw rate change velocity of the vehicle will be low.Hence, in the situation wherein the sensitivity of the lateralacceleration, the longitudinal acceleration or the yaw rate changevelocity in response to a change in the μ is low, it is considereddesirable to restrain the updating of the estimated value of μ on thebasis of the difference between the estimated value and the detectedvalue of each of the lateral acceleration, the longitudinal accelerationor the yaw rate change velocity of the vehicle or on the basis of amagnitude relationship between the estimated value and the detectedvalue.

However, the techniques disclosed in patent documents 1 and 2 mentionedabove do not take the aforesaid sensitivity into account. This leads toa possibility that the estimated value of μ is undesirably updatedunduly even when the sensitivity of the lateral acceleration, thelongitudinal acceleration or the yaw rate change velocity in response toa change in μ is low. As a result, the estimated value of μinconveniently exhibits unstable changes or the accuracy of theestimated value of the μ undesirably deteriorates.

SUMMARY OF THE INVENTION

The present invention has been made in view of the background describedabove, and an object of the present invention is to provide a roadsurface frictional coefficient estimating apparatus capable ofestimating the frictional coefficient of a road surface on which avehicle is traveling while restraining an estimated value of thefrictional coefficient from developing unstable changes and alsorestraining deterioration in the accuracy of the estimated value.

To this end, a road surface frictional coefficient estimating apparatusin accordance with the present invention is a road surface frictionalcoefficient estimating apparatus which estimates a frictionalcoefficient of a road surface on which a vehicle is traveling whileupdating the frictional coefficient, including:

a first estimator of a to-be-compared external force which defines apredetermined type of external force component acting on a vehicle dueto the resultant force of road surface reaction forces acting on eachwheel of the vehicle from a road surface as an external force to becompared and determines a first estimated value of the to-be-comparedexternal force by using a friction characteristic model indicating arelationship between a slip between a wheel of the vehicle and the roadsurface and a road surface reaction force, an estimated value of africtional coefficient already determined, and an observed value of apredetermined type of amount to be observed, which is related to abehavior of the vehicle;

a second estimator of a to-be-compared external force which determines avalue of an external force component balancing out an inertial forcecorresponding to the to-be-compared external force on the basis of anobserved value of a motional state amount of the vehicle that definesthe inertial force, which is a part of an inertial force generated by amotion of the vehicle, and obtains the determined value of the externalforce component as a second estimated value of the to-be-comparedexternal force;

a frictional coefficient increasing/decreasing manipulated variabledeterminer which determines an increasing/decreasing manipulatedvariable of an estimated value of the frictional coefficient of the roadsurface on the basis of at least the first estimated value and thesecond estimated value; and

a frictional coefficient estimated value updater which determines a newestimated value of a frictional coefficient by updating the estimatedvalue of the frictional coefficient of the road surface on the basis ofthe increasing/decreasing manipulated variable,

wherein the frictional coefficient increasing/decreasing manipulatedvariable determiner comprises an updating cancellation conditiondeterminer which determines whether or not a predetermined updatingcancellation condition applies, the condition including at least acondition that the first estimated value and the second estimated valuehave opposite polarities against each other, and determines theincreasing/decreasing manipulated variable on the basis of at least adifference between the first estimated value and the second estimatedvalue such that the difference therebetween is converged to zeroprovided that at least a determination result of the updatingcancellation condition determiner is negative, and determines eitherzero or a manipulated variable of a predetermined value for incrementingthe estimated value of the frictional coefficient as theincreasing/decreasing manipulated variable in the case where thedetermination result is affirmative (a first aspect of the invention).

The term “observed value” in the present invention means a detectedvalue directly observed from a sensor output or an estimated valueindirectly observed by using an appropriate model or a natural law fromone or more sensor outputs related to an amount to be observed. Thisapplies to other aspects of the invention, which will be discussedhereinafter, in addition to the first aspect of the invention.

According to the first aspect of the invention, the first estimator ofthe to-be-compared external force determines the estimated value of theto-be-compared external force by using a friction characteristic modelindicating a relationship between a slip between a wheel of a vehicleand a road surface and a road surface reaction force, the estimatedvalue of the frictional coefficient that has already been determined(hereinafter referred to as “the determined estimated value” in somecases), and the observed value of a predetermined type of amount to beobserved, which is related to a behavior of the vehicle.

Thus, the first estimated value is determined as the value of theto-be-compared external force identified depending upon the determinedestimated value of the frictional coefficient.

In this case, more specifically, the road surface reaction force actingon each wheel of the vehicle can be estimated by identifying, i.e.,estimating, the aforesaid slip in the friction characteristic model fromthe observed value of the predetermined type of the amount to beobserved, which is related to a behavior of the vehicle, then supplyingthe identified slip and the determined estimated value of the frictionalcoefficient to the friction characteristic model. Then, the value of theto-be-compared external force determined from the estimated road surfacereaction force may be obtained as a first estimated value.

Hence, the observed value of the predetermined type of amount to beobserved may be the observed value of an amount to be observed that isnecessary to identify the slip between a wheel and a road surface in thefriction characteristic model. The amount to be observed is selectedbeforehand according to the construction of the friction characteristicmodel.

For example, a slip rate of each wheel, a side slip angle, or the likemay be used as an index value indicative of the slip between a wheel anda road surface. Similarly, for example, a translational force in apredetermined direction acting on the entire vehicle due to the roadsurface reaction force, a moment about a predetermined axis, or the likemay be used as the to-be-compared external force.

The determined estimated value of the frictional coefficient ispreferably a latest value among determined estimated values. However,the value may be older than the latest value if the value lies in asufficiently short time of period wherein the estimated value of thefrictional coefficient is maintained substantially constant.

Meanwhile, the second estimator of to-be-compared external forcedetermines the value of an external force component that balances out aninertial force from an observed value of a motional state amount of thevehicle that defines the inertial force corresponding to theto-be-compared external force in the inertial force produced by a motionof the vehicle. The second estimator then obtains the determined valueof the external force component as a second estimated value of theto-be-compared external force.

This makes it possible to determine the second estimated value of theto-be-compared external force from the observed value of the motionalstate amount of the vehicle that defines the inertial forcecorresponding to the to-be-compared external force without using theestimated value of the frictional coefficient of a road surface.

The first aspect of the invention determines an increasing/decreasingmanipulated variable of the estimated value of the frictionalcoefficient of the road surface by the frictional coefficientincreasing/decreasing manipulated variable determiner on the basis of atleast the first estimated value and the second estimated value. Further,the first aspect of the invention updates the estimated value of thefrictional coefficient of a road surface by the frictional coefficientestimated value updater updates the estimated value of the frictionalcoefficient of a road surface on the basis of the increasing/decreasingmanipulated variable. Thus, a new estimated value of the frictionalcoefficient is determined.

Here, the first estimated value and the second estimated value mentionedabove carry a meaning as the estimated values of the same to-be-comparedexternal force. Therefore, if the first estimated value and the secondestimated value have polarities that are opposite from each other, thenat least one of the first estimated value and the second estimated valueis likely to exhibit low reliability as the estimated value of theto-be-compared external force. This means that the difference betweenthe first estimated value and the second estimated value is highlyunlikely to properly reflect an error of the determined estimated valueof the frictional coefficient.

According to the first aspect of the invention, therefore, thefrictional coefficient increasing/decreasing manipulated variabledeterminer determines by the updating cancellation condition determinerwhether a predetermined updating cancellation condition, which includesat least a condition that the first estimated value and the secondestimated value have polarities that are opposite from each other,applies.

The frictional coefficient increasing/decreasing manipulated variabledeterminer determines the increasing/decreasing manipulated variable onthe basis of at least the difference between the first estimated valueand the second estimated value such that the difference therebetween isconverged to zero, provided that the determination result of at leastthe updating cancellation condition determiner is negative. If thedetermination result is affirmative, then the frictional coefficientincreasing/decreasing manipulated variable determiner determines eitherzero or a manipulated variable of a predetermined value for incrementingthe estimated value of the frictional coefficient as theincreasing/decreasing manipulated variable.

Thus, according to the first aspect of the invention, if the firstestimated value and the second estimated value have opposite polaritiesand the difference therebetween is highly unlikely to properly reflectan error of a determined estimated value of the frictional coefficient,then the increasing/decreasing manipulated variable will not bedetermined on the basis of the difference. To be more specific, theincreasing/decreasing manipulated variable will be determined to zero orthe manipulated variable of the predetermined value for increasing theestimated value of the frictional coefficient without depending upon thedifference.

As a result, in the case where the first estimated value and the secondestimated value have polarities opposite to each other, it is possibleto prevent the estimated value of the frictional coefficient from beingupdated on the basis of an improper increasing/decreasing manipulatedvariable. This allows the frictional coefficient to be estimated whilerestraining the estimated value of the frictional coefficient of a roadsurface on which the vehicle is traveling from developing unstablechanges or restraining the accuracy of the estimated value fromdeteriorating.

According to the first aspect of the invention, preferably, in the casewhere the determination result given by the updating cancellationcondition determiner has changed from “affirmative” over to “negative,”the frictional coefficient increasing/decreasing manipulated variabledeterminer determines the increasing/decreasing manipulated variable onthe basis of at least the difference, provided that a status wherein thedetermination result remains negative lasts for predetermined time ormore after the changeover, and determines, as the increasing/decreasingmanipulated variable, either zero or a manipulated variable of apredetermined value for incrementing the estimated value of thefrictional coefficient until a status in which the determination resultis negative lasts for the predetermined time (a second aspect of theinvention).

More specifically, when the determination result given by the updatingcancellation condition determiner has changed from affirmative tonegative, the changeover may have been temporarily caused by a change inan error component included in the first estimated value or the secondestimated value. In such a case, the difference between the firstestimated value and the second estimated value is highly likely to bestill least dependent upon the error of the determined estimated valueof the frictional coefficient.

According to the second aspect of the invention, therefore, determiningthe increasing/decreasing manipulated variable on the basis of thedifference is not carried out until the status wherein at least thedetermination result of the updating cancellation condition determineris negative lasts for the predetermined time. To be more specific, inthis status, the increasing/decreasing manipulated variable isdetermined to be zero or the aforesaid predetermined value, as with thecase where the determination result is affirmative.

This arrangement makes it possible to securely prevent the estimatedvalue of the frictional coefficient of a road surface on which a vehicleis traveling from developing unstable changes and to securely preventthe accuracy of the estimated value from deteriorating immediately afterthe status in which the determination result of the updatingcancellation condition determiner is affirmative is switched to thestatus in which the determination result is negative.

In the first aspect and the second aspect of the invention describedabove, the updating cancellation condition preferably further includes acondition that at least one of the first estimated value and the secondestimated value lies within a predetermined range that has been presetas a range in the vicinity of zero (a third aspect of the invention).

More specifically, in the situation wherein the magnitude of the actualvalue of the to-be-compared external force is zero or close thereto, thefirst estimated value or the second estimated value tends to includerelatively many error components (i.e., the situation wherein the S/Nratio of the first estimated value or the second estimated value tendsto decrease). In such a case, the difference between the first estimatedvalue and the second estimated value is highly likely to be still leastdependent upon the error of the determined estimated value of thefrictional coefficient.

According to the third aspect of the invention, therefore, the updatingcancellation condition applies not only in the case where the firstestimated value and the second estimated value have polarities that areopposite to each other but also in the case where at least one of thefirst estimated value and the second estimated value falls within theaforesaid predetermined range in the vicinity of zero.

This arrangement makes it possible to securely prevent the estimatedvalue of the frictional coefficient of a road surface on which a vehicleis traveling from developing unstable changes and also to securelyprevent the accuracy of the estimated value from deteriorating in thesituation wherein the magnitude of the actual value of theto-be-compared external force is zero or close thereto (i.e., the S/Nratio of the first estimated value or the second estimated value tendsto lower).

In the road surface frictional coefficient estimating apparatusaccording to the present invention, in the case where the updatingcancellation condition includes a plurality of conditions, if thedetermination result of the updating cancellation condition determineris affirmative, then it means that at least one of the plurality ofconditions applies. This will apply to other aspects of the invention,which will be discussed hereinafter, in addition to the third aspect ofthe invention.

Preferably, the first to the third aspects of the invention include a μsensitivity calculator which determines the value of a μ sensitivitywhich indicates the ratio of an incremental amount of the to-be-comparedexternal force relative to an incremental amount of the frictionalcoefficient of a road surface, or the value of a t sensitivity obtainedby dividing the ratio by the value of the frictional coefficient of theroad surface, wherein the updating cancellation condition furtherincludes a condition that the value of the μ sensitivity has a polaritythat is opposite from that of at least one of the first estimated valueand the second estimated value (a fourth aspect of the invention).

Here, according to the study by the inventor of the present application,if an appropriate type of external force component is selected as theto-be-compared external force, then the actual value of theto-be-compared external force tends to carry the same polarity as thatof the value of the μ sensitivity. Therefore, if at least one of thefirst estimated value and the second estimated value has a polarityopposite from that of the value of the μ sensitivity, then the firstestimated value or the second estimated value includes relatively manyerror components. Consequently, the dependency of the difference betweenthe first estimated value and the second estimated value is highlylikely to be low relative to an error of a determined estimated value ofthe frictional coefficient.

According to the fourth aspect, therefore, the updating cancellationcondition is applied not only in the case where the first estimatedvalue and the second estimated value have polarities that are oppositeto each other but also in the case where the value of the μ sensitivityhas a polarity opposite from that of at least one of the first estimatedvalue and the second estimated value. This arrangement makes it possibleto securely prevent the estimated value of the frictional coefficient ofa road surface on which a vehicle is traveling from developing unstablechanges and also securely prevent the accuracy of the estimated valuefrom deteriorating.

In the fourth aspect of the invention, an appropriate example of theto-be-compared external force may be a moment about a yaw axis at apredetermined point (e.g., a neutral steer point, which will bedescribed later) of a vehicle or the resultant force of the road surfacereaction forces (a driving/braking force and a lateral force, or lateralforces) acting on a front wheel of the vehicle.

In the aforesaid fourth aspect of the invention, the updatingcancellation condition preferably further includes a condition that thevalue of the μ sensitivity is a value within a predetermined range thathas been preset as a range in the vicinity of zero (a fifth aspect ofthe invention).

More specifically, the value of the μ sensitivity being close to zeromeans that the sensitivity of change in the value of the to-be-comparedexternal force relative to a change in the frictional coefficient of aroad surface is low, that is, it is difficult for a change in thefrictional coefficient to be reflected on the value of theto-be-compared external force. In such a situation, an error of thedetermined estimated value of the frictional coefficient is hardlyreflected on the difference between the first estimated value and thesecond estimated value.

According to the fifth aspect of the invention, therefore, the updatingcancellation condition is applied also in the case where the value ofthe μ sensitivity lies within a predetermined range in the vicinity ofzero. This arrangement makes it possible to securely prevent theestimated value of the frictional coefficient of a road surface on whicha vehicle is traveling from developing unstable changes and alsosecurely prevent the accuracy of the estimated value from deterioratingin the situation wherein a change in the frictional coefficient ishardly reflected on the value of a to-be-compared external force.

Further, in the fourth or the fifth aspect of the invention in which thevalue of the μ sensitivity is used in the processing carried out by theupdating cancellation condition determiner, when determining theincreasing/decreasing manipulated variable on the basis of the aforesaiddifference, the frictional coefficient increasing/decreasing manipulatedvariable determiner preferably determines the increasing/decreasingmanipulated variable on the basis of the difference and the value of theμ sensitivity (a sixth aspect of the invention).

More specifically, as the value of the μ sensitivity becomes closer tozero, the actual to-be-compared external force becomes less susceptibleto the influence of a change in the frictional coefficient of an actualroad surface. Hence, it is considered desirable to decrease themagnitude of a gain value (feedback gain), which indicates the ratio ofa change in the increasing/decreasing manipulated variable relative to achange in the difference between the first estimated value and thesecond estimated value, as the magnitude of the μ sensitivity decreasesin the case where the increasing/decreasing manipulated variable isdetermined on the basis of the difference.

According to the sixth aspect of the invention, therefore, theincreasing/decreasing manipulated variable is determined on the basis ofthe difference and the value of the μ sensitivity. This arrangementmakes it possible to determine the increasing/decreasing manipulatedvariable such that the magnitude of the gain value decreases as themagnitude of the μ sensitivity decreases. Consequently, it is possibleto prevent the estimated value of the frictional coefficient from beingunduly changed in the situation wherein the magnitude of the μsensitivity decreases.

In the sixth aspect of the invention, more specifically, in the case ofdetermining the increasing/decreasing manipulated variable on the basisof the difference, the frictional coefficient increasing/decreasingmanipulated variable determiner preferably determines theincreasing/decreasing manipulated variable on the basis of the productof the difference and the μ sensitivity, namely, the product of thevalue of the difference and the value of the μ sensitivity or theproduct of the difference and the μ sensitivity, namely, the product ofthe difference and a μ-sensitivity-dependent value, which is obtained bypassing the value of the μ sensitivity through one or both of a thirdfilter for regulating frequency components and a saturationcharacteristic element (a seventh aspect of the invention).

As the third filter, filters having a high-cut characteristic (low-passcharacteristic), a low-cut characteristic (high-pass characteristic) ora band-pass characteristic may be used. Further, the saturationcharacteristic element is an element that has a characteristic in whichthe ratio of a change in an output of the saturation characteristicelement relative to a change in the value of the μ sensitivity decreasesas the magnitude of the value (absolute value) of the μ sensitivityincreases. In this case, the ratio of the change in the output of thesaturation characteristic element relative to the change in the value ofthe μ sensitivity may change continuously or discontinuously with achanging magnitude of the value of the μ sensitivity.

According to the seventh aspect of the invention, the product of thedifference and the μ sensitivity approaches zero as the magnitude of thevalue of the μ sensitivity approaches zero. Hence, theincreasing/decreasing manipulated variable can be determined such thatthe magnitude of the gain value decreases as the value of the μsensitivity approaches zero by determining the increasing/decreasingmanipulated variable on the basis of the product of the difference andthe μ sensitivity.

Further, in the seventh aspect of the invention, more specifically, thefrictional coefficient increasing/decreasing manipulated variabledeterminer preferably determines the increasing/decreasing manipulatedvariable on the basis of the product of the difference and the μsensitivity such that the increasing/decreasing manipulated variable isproportional to the product of the difference and the μ sensitivity (aneighth aspect of the invention).

According to the eighth aspect of the invention, theincreasing/decreasing manipulated variable will be proportional to theproduct of the difference and the μ sensitivity. Hence, theincreasing/decreasing manipulated variable will be determined toapproach zero as the value of the μ sensitivity approaches zero.

Further, in the first to the eighth aspects of the invention, theto-be-compared external force is ideally a moment about a yaw axis at aneutral steer point (hereinafter referred to as “NSP” in some cases) ofa vehicle (hereinafter referred to as “the NSP yaw moment” in somecases) (a ninth aspect of the invention).

According to a finding of the inventor of the present application, theNSP yaw moment is dependent upon the frictional coefficient of a roadsurface while at the same time almost immune to the influence of thestate amount of the side slip motion of the center of gravity of thevehicle or the bank angle of the road surface. For this reason, when theNSP yaw moment is defined as the to-be-compared external force, thedifference between the first estimated value and the second estimatedvalue will be more dependent upon an error of the determined estimatedvalue of the frictional coefficient. Therefore, theincreasing/decreasing manipulated variable that makes it possible toproperly eliminate the error of the estimated value of the frictionalcoefficient can be determined by determining the increasing/decreasingmanipulated variable on the basis of at least the difference such thatthe difference is converged to zero. This makes it possible to enhancethe accuracy and stability of the estimated value of the frictionalcoefficient.

If the NSP yaw moment is used as the to-be-compared external force, aswith the ninth aspect of the invention, an acceleration sensor thatgenerates an output based on lateral acceleration of the vehicle isdesirably provided and an observed value of a motional state amount ofthe vehicle used for determining the second estimated value of the NSPyaw moment desirably includes the observed value of the accelerationindicated by an output of the acceleration sensor (an output based onthe lateral acceleration of the vehicle). This arrangement generallycauses the acceleration sensor to sense also gravitational acceleration.Thus, if a road surface has a bank angle (non-zero bank angle), then theobserved value of the acceleration indicated by an output of theacceleration sensor will include a component attributable to aninfluence of the bank angle. With this arrangement, the second estimatedvalue of the NSP yaw moment can be properly determined, including thecomponent attributable to the influence of the bank angle, without theneed for the value of the bank angle.

Supplementally, if the NSP yaw moment is used as the to-be-comparedexternal force, then the first estimator of a to-be-compared externalforce uses, for example, the observed value of a state amount related toa rotational motion about the yaw axis of the vehicle (e.g., theobserved value of a yaw rate or the observed value of the temporalchange rate of the yaw rate) and the value of the lateral accelerationof the vehicle indicated by an output of the acceleration sensor as theobserved values of the motional state amount, thereby determining theNSP yaw moment from these observed values. If, for example, the lateralacceleration of the center-of-gravity point of the vehicle is observed(detected) by the acceleration sensor and the yaw rate of the vehicle isobserved (detected) by a yaw rate sensor, then the moment combining themoment obtained by multiplying the observed value of the acceleration bythe mass of the vehicle and the distance between the center-of-gravitypoint of the vehicle to the NSP and the moment obtained by multiplyingthe temporal change rate of the observed value of the yaw rate (adifferential value) by the inertial moment about the yaw axis at thecenter-of-gravity point of the vehicle will be the second estimatedvalue of the NSP yaw moment.

The NSP yaw moment is generated on the basis of a lateral force of aroad surface reaction force acting on each wheel (a translational forcecomponent in the lateral direction of the wheel) and a driving/brakingforce (a translational force component in the longitudinal direction ofthe wheel), and is highly dependent particularly upon the lateral force.Accordingly, the second estimator of the to-be-compared external forcedetermines the first estimated value of the NSP yaw moment, for example,as described below.

Based on the aforesaid friction characteristic model, the determinedestimated value of the frictional coefficient, and the observed value ofan amount to be observed, the second estimator of the to-be-comparedexternal force estimates the lateral force of a road surface reactionforce acting on each wheel of the vehicle or both the lateral force andthe driving/braking force. Then, the estimated value of the lateralforce or the estimated values of the lateral force and thedriving/braking force are used to determine the first estimated value ofthe NSP yaw moment.

More specifically, the friction characteristic model used to estimatethe lateral force of each wheel may be, for example, a model thatindicates a relationship among the slip rate of each wheel of thevehicle or the driving/braking force of a road surface reaction forceacting on the wheel, the lateral force of the road surface reactionforce, a side slip angle of the wheel, and the frictional coefficient ofa road surface. In this case, the amounts to be observed necessary foridentifying the slip rate of each wheel or the driving/braking force andthe side slip angle may be selected as the predetermined types ofamounts to be observed.

Further, to estimate the lateral force of each wheel and thedriving/braking force, for example, a first model that indicates arelationship among the slip rate of each wheel of the vehicle, thedriving/braking force of the road surface reaction force acting on thewheel, the side slip angle of the wheel, and the frictional coefficientof a road surface and a second model that indicates a relationship amongthe slip rate of each wheel of the vehicle or the driving/braking forceof the road surface reaction force acting on the wheel, the lateralforce of the road surface reaction force, the side slip angle of thewheel, and the frictional coefficient of the road surface may be used asthe friction characteristic models. In this case, the amounts to beobserved necessary for identifying the slip rate of each wheel and theside slip angle may be selected as the predetermined types of amounts tobe observed.

As the technique for estimating the slip rate of each wheel (or thedriving/braking force) and the side slip angle, a publicly knowntechnique may be used.

In the fourth to the eighth aspects of the invention provided with the μsensitivity calculator, in the case where the NSP yaw moment is used asthe to-be-compared external force, the μ sensitivity calculatorpreferably determines the value of the μ sensitivity by linearlycoupling the observed value of a steering angle of a steering controlwheel among the wheels of the vehicle and the observed value of the yawrate of the vehicle (a tenth aspect of the invention).

More specifically, according to the study by the inventor of the presentapplication, in a state wherein the vehicle is traveling straight or ina state similar thereto, that is, if the actual yaw rate and side slipangle of the vehicle are both zero or close to zero, then the magnitudeof the μ sensitivity tends to decrease. Further, the μ sensitivity canbe approximately estimated by linearly coupling the observed value ofthe steering angle of a steering control wheel of the wheels of thevehicle and the observed value of the yaw rate of the vehicle. In thiscase, the μ sensitivity determined by the linear coupling will be zeroor close thereto without being influenced by a bank angle or the like ofa road surface in a situation wherein the vehicle is traveling straightor nearly straight.

Thus, according to the tenth aspect of the invention, the magnitude ofthe value of the μ sensitivity calculated by the μ sensitivitycalculator can be reduced in the situation wherein the vehicle istraveling straight or nearly straight. This consequently makes itpossible to determine the increasing/decreasing manipulated variablesuch that the magnitude of the gain value is small in the aforesaidsituation. Thus, it is possible to restrain the estimated value of thefrictional coefficient from being unduly changed in the aforesaidsituation.

In the tenth aspect of the invention, further preferably, the μsensitivity calculator sets at least one of a weighting factor appliedto the observed value of the steering angle and a weighting factorapplied to the observed value of the yaw rate in the linear couplingaccording to the observed value of a vehicle speed such that the mutualratio of both weighting factors changes according to the vehicle speedof the vehicle, and uses the set weighting factor to carry out thecalculation of the linear coupling (an eleventh aspect of theinvention).

With this arrangement, the reliability of the value of the μ sensitivitycalculated by the μ sensitivity calculator can be enhanced, thus makingit possible to ideally determine the increasing/decreasing manipulatedvariable on which the value of the μ sensitivity has been reflected.

The μ sensitivity calculator in the eleventh aspect of the invention iscapable of properly determining a reliable μ sensitivity value fordetermining the increasing/decreasing manipulated variable by thecalculation of the linear coupling represented by, for example, anexpression 5-7, which will be discussed hereinafter.

In this case, the linear coupling represented by expression 5-7 will be,in other words, configured to be the linear coupling in which, forexample, the value of the sensitivity is determined such that the valueof the μ sensitivity is proportional to the value of the NSP yaw momentidentified using a linear two-wheeled vehicle model from the observedvalue of the steering angle of a steering control wheel among the wheelsof the vehicle, the observed value of the yaw rate of the vehicle, andthe observed value of the vehicle speed of the vehicle in the case wherethe frictional coefficient of a road surface takes a constant value, thelinear two-wheeled vehicle being adapted to approximately represent theside slip motion and the rotational motion about the yaw axis of anactual vehicle as a behavior of a model vehicle having a front wheel asa steering control wheel and a rear wheel as a non-steering controlwheel.

In the ninth to the eleventh aspects of the invention in which the NSPyaw moment is used as the to-be-compared external force, morespecifically, the first estimator of the to-be-compared external forceis constructed, for example, as described below. The first estimator ofthe to-be-compared external force includes a vehicle motion/road surfacereaction force estimator which estimates at least the lateral force ofthe road surface reaction force acting on each wheel while estimating atleast the side slip motional state amount of the motional state amountof the vehicle generated by the resultant force of the road surfacereaction forces acting on each wheel of the vehicle, and determines thefirst estimated value of the moment about the yaw axis at the neutralsteer point by using the estimated value of the lateral force that hasbeen determined by the vehicle motion/road surface reaction forceestimator, and the vehicle motion/road surface reaction force estimatorincludes a device which determines the estimated value of a side slipangle as the slip of each wheel of the vehicle by using the observedvalue of the amount to be observed and the estimated value of the sideslip motional state amount of the vehicle that has already beendetermined, a device which supplies at least the estimated value of theside slip angle of each wheel and the estimated value of the frictionalcoefficient of the road surface that has been already determined to thefriction characteristic model so as to determine the estimated value ofthe lateral force acting on each wheel by the friction characteristicmodel, and a device which determines a new estimated value of the sideslip motional state amount of the vehicle by using a dynamicrelationship between the resultant force of road surface reaction forcesincluding at least the lateral force acting on each wheel and the sideslip motional state amount of the vehicle and the estimated value of thelateral force acting on each wheel (a twelfth aspect of the invention).

In the twelfth aspect of the invention, the vehicle motion/road surfacereaction force estimator uses the observed value of the amount to beobserved and the estimated value of the side slip motional state amountof the vehicle that has already been determined, thereby determining theestimated value of the side slip angle indicative of the slip of eachwheel of the vehicle.

In this case, the side slip motional state amount of the vehicle is, forexample, the side slip angle of the center-of-gravity point of thevehicle or a side slip velocity thereof. The estimated value of the sideslip motional state amount of the vehicle that has already beendetermined (hereinafter referred to as the “determined estimated value”in some cases) is preferably the latest value among the determinedestimated values. However, the value may be older than the latest valueif the value lies in a sufficiently short period of time wherein theside slip motional state amount is maintained substantially constant.

As the observed value of the amount to be observed, the observed valueof the amount to be observed that is necessary for estimating the sideslip angle of each wheel (e.g., the yaw rate of the vehicle, thesteering angle of a steering control wheel, and a vehicle speed) may beused in combination with the determined estimated value of the side slipmotional state amount of the vehicle. For example, the estimated valueof the moving speed of a ground contact portion of each wheel can bedetermined from the observed value of a vehicle speed, the determinedestimated value of a side slip motional state amount of the vehicle, andthe observed value of the yaw rate of the vehicle. Furthermore, theestimated value of the side slip angle of each of the wheels, includingthe steering control wheels, can be determined from the estimated valueof the moving speed and the observed value of the steering angle of thesteering control wheel.

Then, the vehicle motion/road surface reaction force estimator inputsthe estimated value of the side slip angle of each wheel and thedetermined estimated value of the frictional coefficient into thefriction characteristic model thereby to determine the estimated valueof a lateral force acting on each wheel by using the frictioncharacteristic model.

Here, the side slip motion of the vehicle is generated primarily due tothe resultant force of the lateral forces acting on the wheels.According to the twelfth aspect of the invention, therefore, the vehiclemotion/road surface reaction force estimator determines the newestimated value of the side slip motional state amount of the vehicle byusing a dynamic relationship between the resultant force of road surfacereaction forces including at least the lateral force acting on eachwheel and the side slip motional state amount of the vehicle (e.g., arelationship represented by a dynamic equation related to the lateraltranslational motion of the center-of-gravity point of the vehicle) andthe estimated value of the lateral force acting on each wheel.

Thus, according to the twelfth aspect of the invention, the lateralforce acting on each wheel can be estimated while estimating the sideslip angle and a side slip motional state amount of the vehiclenecessary to estimate the lateral force. In this case, as describedabove, the NSP yaw moment is hardly affected by the influence of theside slip motional state amount of the center of gravity of the vehicle.Hence, the estimation of the side slip motional state amount of thevehicle and the estimation of the frictional coefficient of a roadsurface can be concurrently performed while restraining an error of theestimated value of the side slip motional state amount from affectingthe accuracy of the estimated value of the frictional coefficient of aroad surface.

Alternatively, in the ninth to the eleventh aspects of the invention,the first estimator of the to-be-compared external force may beconstructed, for example, as described below. The first estimator of theto-be-compared external force includes a vehicle motion/road surfacereaction force estimator which estimates the driving/braking force andthe lateral force of a road surface reaction force acting on each wheelwhile estimating at least the side slip motional state amount of themotional state amounts of the vehicle generated by the resultant forceof the road surface reaction forces acting on each wheel of the vehicle,and determines a first estimated value of a moment about the yaw axis atthe neutral steer point by using the estimated value of the lateralforce determined by the vehicle motion/road surface reaction forceestimator, and the vehicle motion/road surface reaction force estimatorincludes a device which determines the estimated values of a slip rateand a side slip angle as the slip of each wheel of the vehicle by usingthe observed value of the amount to be observed and the estimated valueof the side slip motional state amount of the vehicle that has alreadybeen determined, a device which supplies at least the estimated valuesof the slip rate and the side slip angle of each wheel and the estimatedvalue of the frictional coefficient of the road surface that has beenalready determined to the friction characteristic model so as todetermine the estimated values of the driving/braking force and thelateral force acting on each wheel by the friction characteristic model,and a device which determines a new estimated value of the side slipmotional state amount of the vehicle by using a dynamic relationshipbetween the resultant force of road surface reaction forces including atleast the driving/braking force and the lateral force acting on eachwheel and the side slip motional state amount of the vehicle and theestimated value of the lateral force acting on each wheel (a thirteenthaspect of the invention).

In the thirteenth aspect of the invention, the vehicle motion/roadsurface reaction force estimator uses the observed value of the amountto be observed and the estimated value of the side slip motional stateamount of the vehicle that has already been determined, therebydetermining the estimated values of the slip rate and the side slipangle indicative of the slip of each wheel of the vehicle.

In this case, the side slip motional state amount of the vehicle is, forexample, the side slip angle of the center-of-gravity point of thevehicle or a side slip velocity thereof. The estimated value of the sideslip motional state amount of the vehicle that has already beendetermined (the determined estimated value) is preferably the latestvalue among the determined estimated values, as with the twelfth aspectof the invention. However, the value may be older than the latest valueif the value lies in a sufficiently short period of time wherein theside slip motional state amount is maintained substantially constant.

As the aforesaid observed value of the amount to be observed, theobserved value of the amount to be observed that is necessary forestimating the slip rate and the side slip angle of each wheel (e.g.,the yaw rate of the vehicle, the steering angle of a steering controlwheel, and a vehicle speed) may be used in combination with thedetermined estimated value of the side slip motional state amount of thevehicle. For example, the estimated value of the moving speed of aground contact portion of each wheel can be determined from the observedvalue of a vehicle speed, the determined estimated value of a side slipmotional state amount of the vehicle, and the observed value of the yawrate of the vehicle. Furthermore, the estimated value of the side slipangle of each wheel, including the steering control wheels, can bedetermined from the estimated value of the moving speed and the observedvalue of the steering angle of the steering control wheel. In addition,the estimated value of the slip rate of each of the wheels, includingthe steering control wheels, can be determined from the estimated valueof the moving speed of the ground contact portion of each wheel, theobserved value of the vehicle speed, and the observed value of thesteering angle of a steering control wheel.

Then, the vehicle motion/road surface reaction force estimator inputsthe estimated values of the side slip angle and the slip rate of eachwheel and the determined estimated value of the frictional coefficientinto the friction characteristic model thereby to determine theestimated value of a lateral force and the driving/braking force actingon each wheel by using the friction characteristic model. Further, thevehicle motion/road surface reaction force estimator determines the newestimated value of the side slip motional state amount of the vehicle byusing a dynamic relationship between the resultant force of road surfacereaction forces including at least the driving/braking force and thelateral force acting on each wheel and the side slip motional stateamount of the vehicle (e.g., a relationship represented by a dynamicequation related to the lateral translational motion of thecenter-of-gravity point of the vehicle) and the estimated values of thedriving/braking force and the lateral force acting on each wheel.

Thus, according to the thirteenth aspect of the invention, thedriving/braking force and the lateral force acting on each wheel can beestimated while estimating the slip rate and the side slip angle of eachwheel and a side slip motional state amount of the vehicle necessary toestimate the driving/braking force and the lateral force. In this case,as with the twelfth aspect of the invention, the estimation of the sideslip motional state amount of the vehicle and the estimation of thefrictional coefficient of a road surface can be concurrently performedwhile restraining an error of the estimated value of the side slipmotional state amount from affecting the accuracy of the estimated valueof the frictional coefficient of a road surface.

In place of the first estimated value and the second estimated value ofthe to-be-compared external force or the value of the μ sensitivity, theroad surface frictional coefficient estimating apparatus in accordancewith the present invention may use the values obtained by passing theseestimated values and the μ sensitivity value through a frequencycomponent regulating filter.

More specifically, the present invention using such a filter isconfigured as described below.

The road surface frictional coefficient estimating apparatus inaccordance with the present invention is a road surface frictionalcoefficient estimating apparatus which estimates a frictionalcoefficient of a road surface, on which a vehicle is traveling, whileupdating the frictional coefficient, including:

a first estimator of a to-be-compared external force which defines apredetermined type of external force component acting on a vehicle dueto a resultant force of road surface reaction forces acting on eachwheel of the vehicle from a road surface as the external force to becompared and which determines a first estimated value of theto-be-compared external force by using a friction characteristic modelindicating a relationship between a slip between a wheel of the vehicleand the road surface and a road surface reaction force, an estimatedvalue of a frictional coefficient already determined (the determinedestimated value), and an observed value of a predetermined type ofamount to be observed, which is related to a behavior of the vehicle;

a second estimator of a to-be-compared external force which determines avalue of an external force component that balances out an inertial forcefrom an observed value of a motional state amount of the vehicle thatdefines the inertial force corresponding to the to-be-compared externalforce of the inertial force produced by a motion of the vehicle, andobtains the determined value of the external force component as a secondestimated value of the to-be-compared external force;

a frictional coefficient increasing/decreasing manipulated variabledeterminer which determines an increasing/decreasing manipulatedvariable of an estimated value of the frictional coefficient of the roadsurface on the basis of at least the first estimated value and thesecond estimated value; and

a frictional coefficient estimated value updater which determines a newestimated value of a frictional coefficient by updating the estimatedvalue of the frictional coefficient of a road surface on the basis ofthe increasing/decreasing manipulated variable,

wherein the frictional coefficient increasing/decreasing manipulatedvariable determiner has an updating cancellation condition determinerwhich determines whether or not a predetermined updating cancellationcondition applies, the condition including at least a condition that afirst estimated filtering value obtained by passing the first estimatedvalue through a first filter for regulating frequency components and asecond estimated filtering value obtained by passing the secondestimated value through a second filter for regulating frequencycomponents carry polarities that are opposite from each other,determines the increasing/decreasing manipulated variable on the basisof at least a difference between the first estimated filtering value andthe second estimated filtering value such that the difference isconverged to zero, provided that a determination result of at least theupdating cancellation condition determiner is negative, and determineseither zero or a manipulated variable of a predetermined value forincreasing the estimated value of the frictional coefficient as theincreasing/decreasing manipulated variable in the case where thedetermination result is affirmative (a fourteenth aspect of theinvention).

As the first filter and the second filter, filters having a high-cutcharacteristic (low-pass characteristic), a low-cut characteristic(high-pass characteristic) or a band-pass characteristic may be used.The characteristics of the first and the second filters desirably have asimilar tendency.

The fourteenth aspect of the invention is associated with the firstaspect of the invention described above, and carries out the processingby the frictional coefficient increasing/decreasing manipulated variabledeterminer by using the first estimated filtering value and the secondestimated filtering value in place of the first estimated value and thesecond estimated value. The processing by the first estimator of ato-be-compared external force, the second estimator of a to-be-comparedexternal force, and the frictional coefficient estimated value updateris the same as that in the first aspect of the invention.

Here, as described in relation to the first aspect of the invention, thefirst estimated value and the second estimated value should basicallycarry the same polarity, so that the first estimated filtering value andthe second estimated filtering value should also carry the samepolarity. According to the fourteenth aspect of the invention,therefore, the frictional coefficient increasing/decreasing manipulatedvariable determiner uses the first estimated filtering value and thesecond estimated filtering value instead of the first estimated valueand the second estimated value in carrying out the same processing asthat in the first aspect, namely, the determination processing by theupdating cancellation condition determiner and the processing fordetermining the increasing/decreasing manipulated variable based on thedetermination result.

Thus, according to the fourteenth aspect of the invention, as with thefirst aspect of the invention, in the case where the first estimatedfiltering value and the second estimated filtering value carrypolarities opposite to each other, that is, in the case where thedifference is highly likely not to properly reflect the error of adetermined estimated value of a frictional coefficient, it is possibleto prevent the estimated value of the frictional coefficient from beingupdated on the basis of an improper increasing/decreasing manipulatedvariable. Consequently, the frictional coefficient can be estimatedwhile restraining the estimated value of the frictional coefficient of aroad surface on which a vehicle is traveling from developing unstablechanges and restraining the accuracy of the estimated value fromdeteriorating.

In addition, the fourteenth aspect of the invention is capable ofrestraining unwanted components, such as noise components or driftcomponents, contained in the first estimated value and the secondestimated value from affecting the estimated value of a frictionalcoefficient by using the first estimated filtering value and the secondestimated filtering value. As a result, the accuracy and the stabilityof the estimated value of the frictional coefficient can be furtherenhanced.

In the fourteenth aspect of the invention, preferably, in the case wherethe determination result given by the updating cancellation conditiondeterminer has changed from “affirmative” over to “negative,” thefrictional coefficient increasing/decreasing manipulated variabledeterminer determines the increasing/decreasing manipulated variable onthe basis of at least the difference, provided that a status wherein thedetermination result remains negative lasts for predetermined time ormore after the changeover, and determines, as the increasing/decreasingmanipulated variable, either zero or a manipulated variable of apredetermined value for incrementing the estimated value of thefrictional coefficient until a status in which the determination resultis negative lasts for the predetermined time (a fifteenth aspect of theinvention).

According to the fifteenth aspect of the invention, as with the secondaspect of the invention described above, it is possible to securelyprevent the estimated value of the frictional coefficient of a roadsurface on which a vehicle is traveling from developing unstable changesand to securely prevent the accuracy of the estimated value fromdeteriorating immediately after the status in which the determinationresult of the updating cancellation condition determiner is affirmativeis switched to the status in which the determination result is negative.

Further, in the fourteenth or the fifteenth aspect of the inventiondescribed above, the updating cancellation condition preferably furtherincludes a condition that at least one of the first estimated filteringvalue and the second estimated filtering value lies within apredetermined range that has been preset as a range in the vicinity ofzero (a sixteenth aspect of the invention).

According to the sixteenth aspect of the invention, as with theaforesaid third aspect of the invention, it is possible to securelyprevent the estimated value of the frictional coefficient of a roadsurface on which a vehicle is traveling from developing unstable changesand also to securely prevent the accuracy of the estimated value fromdeteriorating in the situation wherein the magnitude of the actual valueof the to-be-compared external force is zero or close thereto (i.e., thesituation wherein the S/N ratio of the first estimated filtering valueor the second estimated filtering value tends to lower).

Preferably, the fourteenth aspect to the sixteenth aspects of theinvention described above include a μ sensitivity calculator whichdetermines the value of a μ sensitivity, which indicates the ratio of anincremental amount of the to-be-compared external force relative to anincremental amount of the frictional coefficient of a road surface, orthe value of a μ sensitivity obtained by dividing the ratio by the valueof the frictional coefficient of the road surface, wherein the updatingcancellation condition further includes a condition that a μ sensitivityfiltering value obtained by passing the value of the μ sensitivitythrough a third filter for regulating frequency components has apolarity that is opposite from that of at least one of the firstestimated filtering value and the second estimated filtering value (aseventeenth aspect of the invention).

As the third filter, a filter having a high-cut characteristic (low-passcharacteristic), a low-cut characteristic (high-pass characteristic) ora band-pass characteristic may be used. In this case, the characteristicof the third filter desirably has a similar tendency to those of thefirst filter and the second filter.

According to the seventeenth aspect of the invention, the determinationprocessing by the updating cancellation condition determiner is carriedout by taking the polarity of the μ sensitivity filtering value intoaccount in addition to the polarities of the first estimated filteringvalue and the second estimated filtering value. This arrangement makesit possible to securely prevent the estimated value of the frictionalcoefficient of a road surface on which a vehicle is traveling fromdeveloping unstable changes and also to securely prevent the accuracy ofthe estimated value from deteriorating, as with the fourth aspect of theinvention. Further, using the μ sensitivity filtering value makes itpossible to restrain the influences of unwanted components included inthe value of the μ sensitivity, thereby enhancing the stability of adetermination result given by the updating cancellation conditiondeterminer.

In the seventeenth aspect of the invention, as with the aforesaid fourthaspect of the invention, an appropriate example of the to-be-comparedexternal force may be a moment about a yaw axis at a predetermined point(e.g., a neutral steer point, which will be described later) of avehicle or the resultant force of the road surface reaction forces (adriving/braking force and a lateral force, or a lateral force) acting ona front wheel of the vehicle.

In the seventeenth aspect of the invention, the updating cancellationcondition preferably further includes a condition that the μ sensitivityfiltering value is a value within a predetermined range that has beenpreset as a range in the vicinity of zero (an eighteenth aspect of theinvention).

As with the fifth aspect of the invention, the eighteenth aspect of theinvention makes it possible to securely prevent the estimated value ofthe frictional coefficient of a road surface on which a vehicle istraveling from developing unstable changes and also securely prevent theaccuracy of the estimated value from deteriorating in the state whereina change in the frictional coefficient is hardly reflected on the valueof a to-be-compared external force.

Further, in the seventeenth aspect or the eighteenth aspect of theinvention described above, when determining the increasing/decreasingmanipulated variable on the basis of the aforesaid difference, thefrictional coefficient increasing/decreasing manipulated variabledeterminer preferably determines the increasing/decreasing manipulatedvariable on the basis of the difference and the μ sensitivity filteringvalue (a nineteenth aspect of the invention).

According to the nineteenth aspect of the invention, as with theaforesaid sixth aspect of the invention, the increasing/decreasingmanipulated variable can be determined while reducing the magnitude ofthe gain value (feedback gain), which indicates the ratio of a change inthe increasing/decreasing manipulated variable relative to a change inthe aforesaid difference as the magnitude of the μ sensitivity filteringvalue decreases. This makes it possible to prevent the estimated valueof the frictional coefficient from being unduly changed in the statewherein the magnitude of the μ sensitivity filtering value is smaller.The influence of unwanted components included in the value of the μsensitivity can be restrained by using the μ sensitivity filteringvalue. This makes it possible to enhance the stability of theincreasing/decreasing manipulated variable to be determined andconsequently enhance the stability of the estimated value of thefrictional coefficient.

In the nineteenth aspect of the invention, more specifically, in thecase of determining the increasing/decreasing manipulated variable onthe basis of the difference, the frictional coefficientincreasing/decreasing manipulated variable determiner preferablydetermines the increasing/decreasing manipulated variable on the basisof the product of the difference and the μ sensitivity, namely, theproduct of the value of the difference and the value of the μsensitivity filtering value or the product of the difference and the μsensitivity, namely, the product of the difference and aμ-sensitivity-dependent value, which is obtained by passing the μsensitivity filtering value through a saturation characteristic element(a twentieth aspect of the invention).

As with the saturation characteristic element in the seventh aspect ofthe invention, the saturation characteristic element in the twentiethaspect of the invention is an element that has a characteristic in whichthe ratio of a change in an output of the saturation characteristicelement relative to a change in the μ sensitivity filtering valuedecreases as the magnitude of the value (absolute value) of the μsensitivity filtering value increases. In this case, the ratio of thechange in the output of the saturation characteristic element relativeto the change in the μ sensitivity filtering value may changecontinuously or discontinuously with a changing magnitude of the μsensitivity filtering value. Further, the μ-sensitivity-dependent valuein the twentieth aspect of the invention may alternatively be obtainedby passing the μ sensitivity value through the saturation characteristicelement and then through the aforesaid third filter.

According to the twentieth aspect of the invention, the product of thedifference and the μ sensitivity approaches zero as the magnitude of theμ sensitivity filtering value approaches zero. Hence, theincreasing/decreasing manipulated variable can be determined such thatthe magnitude of the gain value decreases as the μ sensitivity filteringvalue approaches zero by determining the increasing/decreasingmanipulated variable on the basis of the product of the difference andthe μ sensitivity, as with the seventh aspect of the invention describedabove.

Further, in the twentieth aspect of the invention, more specifically,the frictional coefficient frictional coefficient increasing/decreasingmanipulated variable determiner preferably determines theincreasing/decreasing manipulated variable on the basis of the productof the difference and the μ sensitivity such that theincreasing/decreasing manipulated variable is proportional to theproduct of the difference and the μ sensitivity (a twenty-first aspectof the invention).

According to the twenty-first aspect of the invention, theincreasing/decreasing manipulated variable will be proportional to theproduct of the difference and the μ sensitivity. Hence, theincreasing/decreasing manipulated variable will be determined toapproach zero as the μ sensitivity filtering value approaches zero.

Further, in the fourteenth to the twenty-first aspects of the invention,the to-be-compared external force is ideally a moment about a yaw axis(an NSP yaw moment) at a neutral steer point (NSP) of a vehicle (atwenty-second aspect of the invention).

According to the twenty-second aspect of the invention, as with theaforesaid ninth aspect of the invention, the difference between thefirst estimated filtering value and the second estimated filtering valuewill be more dependent upon an error of the determined estimated valueof the frictional coefficient. Therefore, the increasing/decreasingmanipulated variable that makes it possible to properly eliminate theerror of the estimated value of the frictional coefficient can bedetermined by determining the increasing/decreasing manipulated variableon the basis of at least the difference such that the difference isconverged to zero. This makes it possible to enhance the accuracy andstability of the estimated value of the frictional coefficient.

In the seventeenth to the twenty-first aspects of the invention providedwith the μ sensitivity calculator, in the case where the NSP yaw momentis used as the to-be-compared external force, the μ sensitivitycalculator preferably determines the value of the μ sensitivity bylinearly coupling the observed value of a steering angle of a steeringcontrol wheel among the wheels of the vehicle and the observed value ofthe yaw rate of the vehicle (a twenty-third aspect of the invention).

Thus, according to the twenty-third aspect of the invention, as with thetenth aspect of the invention described above, the magnitude of thevalue of the μ sensitivity calculated by the μ sensitivity calculatorcan be reduced in the situation wherein the vehicle is travelingstraight or nearly straight. This consequently makes it possible todetermine the increasing/decreasing manipulated variable such that themagnitude of the gain value is small in the aforesaid situation. Thus,it is possible to restrain the estimated value of the frictionalcoefficient from being unduly changed in the aforesaid situation.

In the twenty-third aspect of the invention, further preferably, the μsensitivity calculator sets at least one of a weighting factor appliedto the observed value of the steering angle and a weighting factorapplied to the observed value of the yaw rate in the linear couplingaccording to the observed value of a vehicle speed such that the mutualratio of both weighting factors changes according to the vehicle speedof the vehicle, and uses the set weighting factor to carry out thecalculation of the linear coupling (a twenty-fourth aspect of theinvention).

With this arrangement, as with the aforesaid eleventh aspect of theinvention, the reliability of the value of the μ sensitivity calculatedby the μ sensitivity calculator can be enhanced, thus making it possibleto ideally determine the increasing/decreasing manipulated variable onwhich the value of the μ sensitivity has been reflected.

As with the aforesaid eleventh aspect of the invention, the μsensitivity calculator in the twenty-fourth aspect of the invention iscapable of properly determining a reliable μ sensitivity value fordetermining the increasing/decreasing manipulated variable by thecalculation of the linear coupling represented by, for example, anexpression 5-7, which will be discussed hereinafter.

Further, in the twenty-second to the twenty-fourth aspects of theinvention described above, the first estimator of the to-be-comparedexternal force is constructed, for example, as described below. Thefirst estimator of the to-be-compared external force includes a vehiclemotion/road surface reaction force estimator which estimates at leastthe lateral force of the road surface reaction force acting on eachwheel while estimating at least the side slip motional state amount ofthe motional state amount of the vehicle generated by the resultantforce of the road surface reaction forces acting on each wheel of thevehicle, and determines the first estimated value of a moment about theyaw axis at the neutral steer point by using the estimated value of thelateral force that has been determined by the vehicle motion/roadsurface reaction force estimator, and the vehicle motion/road surfacereaction force estimator includes a device which determines theestimated value of a side slip angle as the slip of each wheel of thevehicle by using the observed value of the amount to be observed and theestimated value of the side slip motional state amount of the vehiclethat has already been determined, a device which supplies at least theestimated value of the side slip angle of each wheel and the estimatedvalue of the frictional coefficient of the road surface that has beenalready determined to the friction characteristic model so as todetermine the estimated value of the lateral force acting on each wheelby the friction characteristic model, and a device which determines anew estimated value of the side slip motional state amount of thevehicle by using a dynamic relationship between the resultant force ofroad surface reaction forces including at least the lateral force actingon each wheel and the side slip motional state amount of the vehicle andthe estimated value of the lateral force acting on each wheel (atwenty-fifth aspect of the invention).

Alternatively, the first estimator of the to-be-compared external forceincludes a vehicle motion/road surface reaction force estimator whichestimates the driving/braking force and the lateral force of the roadsurface reaction force acting on each wheel while estimating at leastthe side slip motional state amount of the motional state amount of thevehicle generated by the resultant force of the road surface reactionforces acting on each wheel of the vehicle, and determines the firstestimated value of a moment about the yaw axis at the neutral steerpoint by using the estimated value of the lateral force that has beendetermined by the vehicle motion/road surface reaction force estimator,and the vehicle motion/road surface reaction force estimator includes adevice which determines the estimated values of a slip rate and a sideslip angle as the slip of each wheel of the vehicle by using theobserved value of the amount to be observed and the estimated value ofthe side slip motional state amount of the vehicle that has already beendetermined, a device which supplies at least the estimated values of theslip rate and the side slip angle of each wheel and the estimated valueof the frictional coefficient of the road surface that has already beendetermined to the friction characteristic model so as to determine theestimated values of the driving/braking force and the lateral forceacting on each wheel by the friction characteristic model, and a devicewhich determines a new estimated value of the side slip motional stateamount of the vehicle by using a dynamic relationship between theresultant force of road surface reaction forces including at least thedriving/braking force and the lateral force acting on each wheel and theside slip motional state amount of the vehicle and the estimated valueof the lateral force acting on each wheel (a twenty-sixth aspect of theinvention).

These twenty-fifth and the twenty-sixth aspects of the invention includethe first estimator of a to-be-compared external force having the sameconstruction as that of the twelfth and the thirteenth aspects of theinvention, respectively. Hence, as with the twelfth and the thirteenthaspects of the invention, according to the twenty-fifth and thetwenty-sixth aspects of the invention, the estimation of the side slipmotional state amount of the vehicle and the estimation of thefrictional coefficient of a road surface can be concurrently performedwhile restraining an error of the estimated value of the side slipmotional state amount of the vehicle from affecting the accuracy of theestimated value of the frictional coefficient of a road surface.

Further, in the case where the present invention includes the aforesaidμ sensitivity calculator, the following mode may be adopted.

A road surface frictional coefficient estimating apparatus in accordancewith the present invention is a road surface frictional coefficientestimating apparatus which estimates a frictional coefficient of a roadsurface on which a vehicle is traveling while updating the frictionalcoefficient, including:

a first estimator of a to-be-compared external force which defines apredetermined type of external force component acting on a vehicle dueto the resultant force of road surface reaction forces acting on eachwheel of the vehicle from a road surface as a to-be-compared externalforce and determines a first estimated value of the to-be-comparedexternal force by using a friction characteristic model indicating arelationship between a slip between a wheel of the vehicle and the roadsurface and a road surface reaction force, an estimated value of africtional coefficient already determined, and an observed value of apredetermined type of amount to be observed, which is related to abehavior of the vehicle;

a second estimator of a to-be-compared external force which determinesthe value of an external force component balancing out an inertial forcefrom an observed value of a motional state amount of the vehicle thatdefines the inertial force corresponding to the to-be-compared externalforce of the inertial force generated by a motion of the vehicle andobtains the determined value of the external force component as a secondestimated value of the to-be-compared external force;

a μ sensitivity calculator which determines the value of a μ sensitivitywhich indicates the ratio of an incremental amount of the to-be-comparedexternal force relative to an incremental amount of the frictionalcoefficient of a road surface, or the value obtained by dividing theratio by the value of the frictional coefficient of the road surface;

frictional coefficient increasing/decreasing manipulated variabledetermining means which determines an increasing/decreasing manipulatedvariable of an estimated value of the frictional coefficient of the roadsurface on the basis of at least a difference between the firstestimated value and the second estimated value or a difference between afirst estimation filtering value obtained by passing the first estimatedvalue through a first filter for regulating frequency components and asecond estimation filtering value obtained by passing the secondestimated value through a second filter for regulating frequencycomponents, and a μ sensitivity value or a μ-sensitivity-dependent valueobtained by passing the μ sensitivity value through one or both of athird filter for regulating frequency components and a saturationcharacteristic element such that the difference is converged to zero;and

a frictional coefficient estimated value updater which determines a newestimated value of a frictional coefficient by updating the estimatedvalue of the frictional coefficient of a road surface on the basis ofthe increasing/decreasing manipulated variable,

wherein the frictional coefficient increasing/decreasing manipulatedvariable determiner determines the increasing/decreasing manipulatedvariable such that the magnitude of the increasing/decreasingmanipulated variable decreases as the magnitude of the μ sensitivityvalue or the μ-sensitivity-dependent value decreases (a twenty-seventhaspect of the invention).

The first to the third filters in the twenty-seventh aspect of theinvention may have the same characteristics as those described inrelation to the fourteenth and the seventeenth aspects of the invention.The saturation characteristic element has the same function as thatdescribed in the seventh or the twentieth aspect of the invention.

As an example of the to-be-compared external force in the twenty-seventhaspect of the invention, the NSP yaw moment described in relation to theninth aspect of the invention may be used.

According to the twenty-seventh aspect of the invention, the firstestimator of the to-be-compared external force and the second estimatorof the to-be-compared external force are the same as those in the firstor the fourteenth aspect of the invention. Hence, the first estimator ofthe to-be-compared external force determines the first estimated valueof a to-be-compared external force. Further, the second estimator of theto-be-compared external force determines the second estimated value ofthe to-be-compared external force without using an estimated value of africtional coefficient.

According to the twenty-seventh aspect of the invention, the frictionalcoefficient increasing/decreasing manipulated variable determinerdetermines the increasing/decreasing manipulated variable of theestimated value of the frictional coefficient of the road surface suchthat the difference between the first estimated value and the secondestimated value or the difference between the first estimation filteringestimated value and the second estimation filtering estimated value isconverged to zero on the basis of at least the difference and the μsensitivity value or the μ-sensitivity-dependent value.

At this time, the increasing/decreasing manipulated variable isdetermined such that the magnitude of the increasing/decreasingmanipulated variable decreases as the magnitude of the μ sensitivityvalue or the μ-sensitivity-dependent value decreases.

Further, the twenty-seventh aspect of the invention determines a newestimated value of a frictional coefficient by updating the estimatedvalue of the frictional coefficient of a road surface on the basis ofthe increasing/decreasing manipulated variable by the frictionalcoefficient estimated value updater.

Here, according to the twenty-seventh aspect of the invention, theincreasing/decreasing manipulated variable is determined such that themagnitude of the increasing/decreasing manipulated variable decreases asthe magnitude of the μ sensitivity value or the μ sensitivity dependentvalue decreases. Therefore, the updating amount of the estimated valueof a frictional coefficient based on the increasing/decreasingmanipulated variable decreases as the magnitude of the μ sensitivityvalue or the μ-sensitivity-dependent value decreases. This restrains theestimated value of the frictional coefficient from being restrained.

In other words, the magnitude of a gain value (feedback gain), whichindicates the ratio of a change in the increasing/decreasing manipulatedvariable relative to a change in the aforesaid difference, is restrainedto be smaller as the magnitude of the μ sensitivity value or theμ-sensitivity-dependent value decreases.

Accordingly, as with the sixth or the nineteenth aspect of theinvention, it is possible to prevent the estimated value of thefrictional coefficient of a road surface from being unduly changed inthe state wherein the magnitude of a μ sensitivity value or aμ-sensitivity-dependent value is smaller (i.e., in the state wherein thedependency of the to-be-compared amount upon the frictional coefficientof a road surface is low). Consequently, the frictional coefficient canbe estimated while preventing the estimated value of the frictionalcoefficient of a road surface on which a vehicle is traveling fromdeveloping unstable changes or the accuracy of the estimated value frombeing deteriorated.

In the twenty-seventh aspect of the invention, as with the seventh orthe twentieth aspect of the invention, the frictional coefficientincreasing/decreasing manipulated variable determiner preferablydetermines the increasing/decreasing manipulated variable on the basisof the product of the difference and the μ-sensitivity-dependent value,which is the product of the difference and the μ sensitivity value orthe μ-sensitivity-dependent value (a twenty-eighth aspect of theinvention). This arrangement makes it possible to provide the sameadvantages as those of the seventh aspect or the twentieth aspect of theinvention.

Further, in the twenty-eighth aspect of the invention, as with theeighth or the twenty-first aspect of the invention, the frictionalcoefficient increasing/decreasing manipulated variable determinerpreferably determines the increasing/decreasing manipulated variable onthe basis of the product of the difference and the μ sensitivity suchthat the increasing/decreasing manipulated variable is proportional tothe product of the difference and the μ sensitivity (a twenty-ninthaspect of the invention). This arrangement makes it possible to providethe same advantages as those of the eighth or the twenty-first aspect ofthe invention.

Further, in the twenty-eighth and the twenty-ninth aspects of theinvention, in the case where the frictional coefficientincreasing/decreasing manipulated variable determiner is a device whichdetermines the increasing/decreasing manipulated variable on the basisof the difference between the first estimation filtering value and thesecond estimation filtering value and the μ-sensitivity-dependent valueobtained by passing the μ sensitivity value through at least the thirdfilter, filters having a low-cut characteristic may be adopted as thefirst filter, the second filter and the third filter (a thirtieth aspectof the invention). Alternatively, filters having a high-cutcharacteristic may be adopted as the first filter, the second filter andthe third filter (a thirty-first aspect of the invention).

The low-cut characteristic more specifically means a frequencycharacteristic that cuts off frequency components of a predeterminedfrequency or less. The high-cut characteristic more specifically means afrequency characteristic that cuts off frequency components of apredetermined frequency or more.

According to the thirtieth aspect of the invention, theincreasing/decreasing manipulated variable can be determined, removinglow frequency or DC error components steadily contained in the firstestimated value, the second estimated value and the μ sensitivityattributable mainly to offsets or drifts of outputs of sensors. Thisarrangement allows the accuracy and stability of the estimated value ofa frictional coefficient to be enhanced. The same applies to the casewhere filters having a low-cut characteristic are adopted as the firstto the third filters in the nineteenth to the twenty-first aspects ofthe invention.

According to the thirty-first aspect of the invention, theincreasing/decreasing manipulated variable can be determined, removinghigh-frequency error components contained in the first estimated value,the second estimated value and the μ sensitivity attributable primarilyto high-frequency noise components contained in outputs of sensors. Thismakes it possible to enhance the accuracy and the stability of theestimated value of a frictional coefficient. The same applies to thecase where filters having a high-cut characteristic are adopted as thefirst to the third filters in the nineteenth to the twenty-first aspectsof the invention.

Supplementally, the first to the third filters may use filters havingboth frequency characteristics, namely, the low-cut characteristic andthe high-cut characteristic (e.g., filters having the band-passcharacteristic).

In the thirty-first aspect of the invention wherein the first to thethird filters have a high-cut characteristic, the frictional coefficientincreasing/decreasing manipulated variable determiner preferablydetermines the increasing/decreasing manipulated variable by passing thepreliminary value of the increasing/decreasing manipulated variablethrough a phase compensation filter having a function for advancing thephase of the preliminary value while determining the preliminary valueon the basis of the difference and the μ-sensitivity-dependent value (athirty-second aspect of the invention). The same applies to the casewhere filters having a high-cut characteristic are adopted as the firstto the third filters in the nineteenth to the twenty-first aspects ofthe invention.

More specifically, in the case where the first to the third filters havea high-cut characteristic, a to-be-compared external force and a μsensitivity tend to incur phase delays in the difference between thefirst estimation filtering value and the second estimation filteringvalue or in the μ-sensitivity-dependent value in a relativelyhigh-frequency area. For this reason, if the difference and theμ-sensitivity-dependent value are used as they are to determine theincreasing/decreasing manipulated variable, then the estimated value ofa frictional coefficient may develop a vibration or the like, causingthe estimated value to be unstable. Therefore, according to thethirty-second aspect of the invention, the phase delay of thepreliminary value is eliminated by passing the preliminary value throughthe phase compensation filter while determining the preliminary value ofthe increasing/decreasing manipulated variable on the basis of thedifference and the μ-sensitivity-dependent value. This makes it possibleto prevent the estimated value of the frictional coefficient of a roadsurface from vibrating and effectively enhance the stability of theestimated value.

In the thirtieth to the thirty-second aspects of the invention, thefrictional coefficient increasing/decreasing manipulated variabledeterminer preferably determines the increasing/decreasing manipulatedvariable on the assumption that the value of the difference is zero inthe case where the difference lies within a predetermined range as arange in the vicinity of zero (a thirty-third aspect of the invention).

More specifically, if the difference between the first estimationfiltering value and the second estimation filtering value takes a valuein the vicinity of zero, then the difference tends to include manycomponents attributable to error components of the first estimated valueand the second estimated value. In other words, the S/N ratio of thedifference tends to become low. Hence, according to the thirty-thirdaspect of the invention, the increasing/decreasing manipulated variableis determined on the assumption that the value of the difference is zeroif the difference lies within a predetermined range as a range in thevicinity of zero. This makes it possible to prevent the estimated valueof a frictional coefficient from being improperly updated, thuspreventing the estimated value from becoming unstable in a situationwherein the S/N ratio of the difference is low.

Further, in the thirtieth to the thirty-second aspects of the invention,the frictional coefficient increasing/decreasing manipulated variabledeterminer preferably determines the increasing/decreasing manipulatedvariable on the assumption that a μ-sensitivity-dependent value is zeroin the case where the μ-sensitivity-dependent value falls within apredetermined range as a range in the vicinity of zero (a thirty-fourthaspect of the invention).

More specifically, in the case where the μ-sensitivity-dependent valueis in the vicinity of zero, the S/N ratio of the μ-sensitivity-dependentvalue is apt to be low. According to the thirty-fourth aspect of theinvention, the increasing/decreasing manipulated variable is determinedon the assumption that the value of the μ-sensitivity-dependent value iszero in the case where the μ-sensitivity-dependent value falls within apredetermined range as a range in the vicinity of zero. This arrangementmakes it possible to prevent the estimated value of a frictionalcoefficient from being improperly updated, thus preventing the estimatedvalue from becoming unstable in a situation wherein the S/N ratio of thedifference is low.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a schematic construction of a vehiclein an embodiment;

FIGS. 2( a) and 2(b) are diagrams visually illustrating representativereference characters used in the description of the embodiment;

FIG. 3 is a block diagram illustrating major functions of a controllerin a first embodiment;

FIG. 4 is a flowchart illustrating the processing by the controller inthe first embodiment;

FIG. 5 is a block diagram illustrating functions of a vehicle modelcalculator illustrated in FIG. 3;

FIGS. 6( a) and 6(b) are graphs for explaining the processing by a wheelslip rate estimator illustrated in FIG. 5;

FIGS. 7( a) and 7(b) are graphs for explaining the processing by a wheelside slip angle estimator illustrated in FIG. 5;

FIG. 8 is a graph for explaining the processing in another mode by thewheel slip rate estimator illustrated in FIG. 5;

FIG. 9 is a flowchart illustrating the processing by a bank angleestimator illustrated in FIG. 3;

FIG. 10 is a flowchart illustrating the processing by a slope angleestimator illustrated in FIG. 3;

FIG. 11 is a block diagram illustrating functions of a μ estimatorillustrated in FIG. 3;

FIG. 12 is a flowchart illustrating the processing by the μ estimatorillustrated in FIG. 3;

FIG. 13 is a flowchart illustrating the processing in S122-5 of FIG. 12;

FIG. 14 is a diagram for explaining the processing for determining africtional coefficient increasing/decreasing manipulated variable Δμ ina second embodiment;

FIG. 15 is a flowchart illustrating the processing for determining thefrictional coefficient increasing/decreasing manipulated variable Δμ inthe second embodiment;

FIG. 16 is a flowchart illustrating the processing for determining thefrictional coefficient increasing/decreasing manipulated variable Δμ ina third embodiment;

FIG. 17 is a flowchart illustrating the processing for determining thefrictional coefficient increasing/decreasing manipulated variable Δμ ina fourth embodiment;

FIG. 18 is a block diagram illustrating a major section of theprocessing for determining the frictional coefficientincreasing/decreasing manipulated variable in a fifth embodiment;

FIG. 19 is a block diagram illustrating a major section of theprocessing for determining the frictional coefficientincreasing/decreasing manipulated variable Δμ in a sixth embodiment;

FIG. 20 is a block diagram illustrating a major section of theprocessing for determining the frictional coefficientincreasing/decreasing manipulated variable Δμ in a seventh embodiment;and

FIG. 21 is a block diagram illustrating a major section of theprocessing for determining the frictional coefficientincreasing/decreasing manipulated variable Δμ in an eighth embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following will describe embodiments of the present invention. First,referring to FIG. 1, a schematic construction of a vehicle in each ofthe embodiments in the present specification will be described.

As illustrated in FIG. 1, a vehicle 1 has a plurality of wheels 2-i(i=1, 2, . . . ), a vehicle body 1B being supported on the wheels 2-i(i=1, 2, . . . ) through suspension devices, which are not shown.

More specifically, the vehicle 1 according to each of the embodimentshas a total of four wheels 2-i (i=1, 2, 3, 4), namely, a pair of rightand left front wheels 2-1, 2-2 and a pair of right and left rear wheels2-3, 2-4. In this case, the front wheels 2-1 and 2-2 among the wheels2-i (i=1, 2, 3, 4) are driving wheels functioning as steering controlwheels, while the rear wheels 2-3 and 2-4 are driven wheels andnon-steering control wheels.

In the following description, the front left wheel 2-1 of the vehicle 1will be referred to as the first wheel 2-1, the front right wheel 2-2will be referred to as the second wheel 2-2, the rear left wheel 2-3will be referred to as the third wheel 2-3, and the rear right wheel 2-4will be referred to as the fourth wheel 2-4 in some cases.

Further, any one wheel among the wheels 2-i (i=1, 2, 3, 4) will berepresented simply as “the wheel 2-i” or “an i-th wheel 2-i,” omittingthe description indicated by (i=1, 2, 3, 4).

A subscript “i” will be added to the reference numeral of an elementrelated to each i-th wheel 2-i among elements (parts, physicalquantities, and the like) other than the wheels 2-i (i=1, 2, 3, 4). Inthis case, for an element corresponding to one particular wheel amongthe wheels 2-i (i=1, 2, 3, 4), the value of i (1 or 2 or 3 or 4)corresponding to a particular wheel will be added in place of thesubscript “i.”

The vehicle 1 has a drive system for rotatively driving the drivingwheels. The drive system has an engine 3 serving as a motive powergenerating source mounted on the vehicle body 1B in each of theembodiments. The drive system transmits the motive power (output torque)of the engine 3 to the front wheels 2-1 and 2-2 serving as the drivingwheels through a motive power transmission mechanism 4, which includes atransmission 4 a, thereby rotatively driving the front wheels 2-1 and2-2. In this case, the motive power of the engine 3 is controlled on thebasis of the manipulated variable of the depression on an accelerator(gas) pedal (not shown) of the vehicle 1.

The vehicle 1 is further provided with a steering system for steeringthe steering control wheels. In each of the embodiments, the steeringsystem has a steering wheel 5 disposed at the front in a driver's seatof the vehicle body 1B. The steering system steers the front wheels 2-1and 2-2 acting as the steering control wheels by a steering mechanism,not shown, according to the rotational operation of the steering wheel 5in an interlocked manner. The steering mechanism is constructed of, forexample, a mechanical steering mechanism, such as a rack and pinion orthe like or a steering mechanism with an actuator, which has a steeringactuator, such as an electric motor (a so-called power steering device).

The vehicle 1 further includes a braking system for braking the travelof the vehicle 1. The braking system in each of the embodiments has africtional braking mechanism 7-i (i=1, 2, 3, 4), such as a disc brake,for each wheel 2-i. Each of these braking mechanisms 7-i (i=1, 2, 3, 4)is connected to a braking system hydraulic circuit 6, and a hydraulicpressure (braking pressure) supplied from the braking system hydrauliccircuit 6 generates a braking force for braking the rotation of acorresponding wheel 2-i.

In this case, the braking system hydraulic circuit 6 basically applies abraking pressure based on a depression manipulated variable (treadingforce) of the brake pedal to each braking mechanism 7-i insynchronization with the operation of depressing the brake pedal (notshown) of the vehicle 1. Further, in the vehicle 1, the braking systemhydraulic circuit 6 is capable of adjusting the braking pressure, i.e.,the braking force on each wheel 2-i) applied to each braking mechanism7-i in response to a control command received from a controller 20,which will be hereinafter described.

The vehicle 1 further includes a variety of sensors for detectingamounts to be observed, which will be discussed later, and thecontroller 20, which mainly controls the behaviors of the vehicle 1 inaddition to the drive system, the steering system, and the brakingsystem.

In each of the embodiments, the vehicle 1 is provided with sensors, suchas wheel rotational angular velocity sensors 8-i (i=1, 2, 3, 4) whichgenerate outputs based on the rotational angular velocity of each wheel2-i, braking pressure sensors 9-i (i=1, 2, 3, 4) which generate outputsbased on the braking pressures supplied to the braking mechanism 7-i ofeach wheel 2-i, a steering control angle sensor 10 which generates anoutput based on the steering angle (rotational angle) of the steeringwheel 5, a transmission sensor 11 which generates an output based on theoperating state (a transmission gear ratio or the like) of thetransmission 3, an accelerator pedal sensor 12 which generates an outputbased on the depression manipulated variable of the accelerator (gas)pedal(not shown) of the vehicle 1, a yaw rate sensor 13 which generatesan output based on a yaw rate, which is an angular velocity about theyaw axis of the vehicle 1 (about the vertical axis of the vehicle body1B), a longitudinal acceleration sensor 14 which generates an outputbased on the acceleration in the direction of the roll axis (thelongitudinal direction of the vehicle body 1B) of the vehicle 1, and alateral acceleration sensor 15 which generates an output based on theacceleration in the direction of the pitch axis of the vehicle 1 (thelateral direction (horizontal direction) of the vehicle body 1B).

The controller 20 is an electronic circuit unit which includes a CPU, aRAM, a ROM and the like, and receives outputs (detection data) of theaforesaid sensors. The controller 20 then carries out predeterminedarithmetic processing based on a program, which has been installedbeforehand, while using the received detection data and set data whichhas been stored and retained in advance, thereby controlling thebehaviors of the vehicle 1.

In this case, the controller 20 has a function for controlling abehavior of the vehicle 1, such as a rotational motion about the yawaxis (turning motion) or a side slip motion, to a desired behavior by,for example, controlling the braking force of each wheel 2-i supplied byeach braking mechanism 7-i through the braking system hydraulic circuit6. The controller 20 also has a function for sequentially estimating africtional coefficient or the like of a road surface on which thevehicle 1 is traveling in order to carry out the processing forcontrolling the behavior of the vehicle 1. The estimated frictionalcoefficient is used to estimate, for example, a state amount of a sideslip motion (a side slip angle, a side slip velocity or the like) of thevehicle 1, or used to determine a desired behavior of the vehicle 1.

The above has described the schematic construction of the vehicle 1 ineach embodiment to be described in the present specification.

The vehicle to which the present invention applies is not limited to thevehicle 1 having the construction described above. For example, themotive power generating source of the drive system of the vehicle 1 maybe an electric motor. Alternatively, both an engine and an electricmotor may be installed in the vehicle 1 as motive power generatingsources.

The driving wheels of the vehicle 1 may alternatively be the rear wheels2-3 and 2-4, or both the front wheels 2-1, 2-2 and the rear wheels 2-3,2-4.

Further, the drive system may be constructed so as to be capable ofindividually adjusting the driving force to be supplied to each drivingwheel from a motive power generating source.

The steering system of the vehicle 1 may be constructed to steer therear wheels 2-3 and 2-4 by actuators as necessary in addition tosteering the front wheels 2-1 and 2-2 in synchronization with therotational operation of the steering wheel 5.

The number of wheels does not have to be four.

Referring now to FIGS. 2( a) and 2(b), major reference characters(variables) and terms used in each embodiment will be described below.

In FIGS. 2( a) and 2(b), variables preceded by “↑”, such as ↑V1 and ↑F1,denote vector amounts. A vector quantity is expressed in the form of acolumn vector (a transposed vector of a row vector) when the componentsthe vector quantity are indicated using an appropriate coordinatesystem.

In the description of each embodiment, “×” is used as the arithmeticsymbol of the multiplication of vector quantities (an exterior product),while “*” is used as the arithmetic symbol of multiplication other thanexterior products, such as the multiplication of scalar quantities orthe multiplication of a scalar quantity and a vector quantity. Toindicate the transposition of a row vector, a superscript “T” will beattached at top right of a component of the row vector.

In a vehicle body coordinate system, the longitudinal direction of thevehicle body 1B is an X-axis direction, while the lateral direction (thehorizontal direction) of the vehicle body 1B is a Y-axis direction. Inthis case, the front direction of the vehicle body 1B is defined as thepositive direction of the X-axis, while the left direction of thevehicle body 1B is defined as the positive direction of the Y-axis.

The X-axis direction of the vehicle coordinate system may be referred tosimply as the longitudinal direction or the direction of the roll axisof the vehicle 1 in some cases. Similarly, the Y-axis direction of thevehicle coordinate system may be referred to simply as the lateraldirection or the direction of the pitch axis of the vehicle 1 in somecases. Further, the direction of the yaw axis of the vehicle 1 (thevertical direction of the vehicle body 1B) is orthogonal to an XY planeof the vehicle body coordinate system (orthogonal to the X-axis and theY-axis).

An i-th wheel coordinate system is a coordinate system in which adirection parallel to the rotational surface of an i-th wheel 2-i (aplane orthogonal to the rotational axis of the i-th wheel 2-i), which isthe longitudinal direction of the i-th wheel 2-i, is defined as thedirection of the x-axis and the direction parallel to the rotationalaxis of an i-th wheel 2-i, which is the horizontal direction (lateraldirection) of the i-th wheel 2-i, is defined as the direction of they-axis when the vehicle 1 is observed from above in the direction of theyaw axis.

In this case, the front direction of the i-th wheel 2-i is defined asthe positive direction of the x-axis and the left direction of the i-thwheel 2-i is defined as the positive direction of the y-axis. An xyplane of the i-th wheel coordinate system is parallel to an XY plane ofthe vehicle body coordinate system and orthogonal to the direction ofthe yaw axis of the vehicle 1.

Supplementally, the term “orthogonal” and “parallel” in the presentspecification do not mean only orthogonal and parallel in strict senses,but the terms may mean approximately orthogonal or parallel.

A reference character “δi” denotes the steering angle (hereinafterreferred to simply as the wheel steering angle) of the i-th wheel 2-i.More specifically, each wheel steering angle δi is an angle formed bythe rotational surface of the i-th wheel 2-i relative to the x-axisdirection of the vehicle body coordinate system when the vehicle 1 isobserved from above in the yaw-axis direction. In the vehicle 1according to the embodiment, the rear wheels 2-3 and 2-4 arenon-steering wheels, so that 53=54=0 always applies.

A reference character “↑Vg” denotes the moving velocity vector of thecenter-of-gravity point of the vehicle 1 relative to a road surface(hereinafter referred to as “the vehicle center of gravity velocityvector”) observed by being projected onto the XY plane of the vehiclecoordinate system. The vehicle center of gravity velocity vector ↑Vg isa vector composed of a component in the x-axis direction and a componentin the y-axis direction of the vehicle body coordinate system. In thiscase, the component in the X-axis direction of the vehiclecenter-of-gravity velocity vector ↑Vg will be denoted by Vgx and will bereferred to as the longitudinal velocity of the vehicle center ofgravity Vgx, and the component in the Y-axis direction will be denotedby Vgy and will be referred to as the side slip velocity of the vehiclecenter of gravity Vgy.

In other words, the longitudinal velocity of the vehicle center ofgravity Vgx means the traveling speed (vehicle speed) of the vehicle 1.Although not shown in FIGS. 2( a) and 2(b), a temporal change rate(differential value) of the longitudinal velocity of the vehicle centerof gravity Vgx will be referred to as the longitudinal velocity changerate of the vehicle center of gravity Vgdot_x and a temporal change rate(differential value) of the side slip velocity of the vehicle center ofgravity Vgy will be referred to as side slip velocity change rate of thevehicle center of gravity Vgdot_y.

A reference character “βg” denotes a side slip angle of thecenter-of-gravity point of the vehicle 1 (hereinafter referred to as thevehicle center-of-gravity side slip angle). More specifically, thevehicle center-of-gravity side slip angle βg is the angle formed by thevehicle center-of-gravity velocity vector ↑Vg with respect to the X-axisdirection of the vehicle body coordinate system. Thus, βg=tan⁻¹(Vgy/Vgx)holds.

A reference character “↑Vi” denotes the moving speed vector of a groundcontact portion of the i-th wheel 2-i relative to a road surface(hereinafter referred to simply as the advancing speed vector of thei-th wheel 2-i or simply as the wheel advancing speed vector). Eachwheel advancing speed vector ↑Vi is a vector composed of a component inthe X-axis direction and a component in the Y-axis direction of thevehicle body coordinate system. In this case, although not shown inFIGS. 2( a) and 2(b), the component in the X-axis direction of eachwheel advancing speed vector ↑Vi will be denoted by Vx_i and thecomponent in the Y-axis direction thereof will be denoted by Vy_i.

A reference character “↑Vsub_i” denotes a moving speed vector of theground contact portion of the i-th wheel 2-i relative to the roadsurface (hereinafter referred to as the wheel advancing speed vector onthe wheel coordinate system), as observed by being projected onto the xyplane of the i-th wheel coordinate system. The wheel advancing speedvector on each wheel coordinate system ↑Vsub_i is a vector composed of acomponent in the x-axis direction and a component in the y-axisdirection of the i-th wheel coordinate system. In this case, althoughnot shown in FIGS. 2( a) and 2(b), the component in the x-axis directionof the wheel advancing speed vector on each wheel coordinate system↑Vsub_i will be denoted by Vsubx_i, while the component in the y-axisdirection of the wheel advancing speed vector on each wheel coordinatesystem ↑Vsub_i will be denoted by Vsuby_i.

The wheel advancing speed vector on each wheel coordinate system ↑Vsub_iof each wheel 2-i and the wheel advancing speed vector ↑Vi are vectorquantities sharing the same spatial orientation and magnitude exceptthat the coordinate systems for representing the vector quantities aredifferent.

A reference character “βi” denotes a side slip angle (hereinafterreferred to simply as the wheel side slip angle in some cases) of thei-th wheel 2-i. More specifically, each wheel side slip angle βi is theangle formed by the wheel advancing speed vector on the wheel coordinatesystem ↑Vsub_i of the i-th wheel 2-i with respect to the x-axisdirection of the i-th wheel coordinate system. Thus,βi=tan⁻¹(Vsuby_i/Vsubx_i) holds.

A reference character “β0 i” denotes an angle formed by the wheeladvancing speed vector ↑Vi of the i-th wheel 2-i with respect to theX-axis direction of the vehicle body coordinate system (=βi+δi:hereinafter referred to as the wheel position side slip angle).

In the embodiment, the rear wheels 2-3 and 2-4 are non-steering wheels,so that β03=β3 and β04=β4 hold. Hence, β03 and β04 are not shown.

A reference character “γ” denotes an angular velocity about the yaw axisof the vehicle 1, that is, the yaw rate.

A reference character “df” denotes the distance between the front wheels2-1 and 2-2 in the lateral direction of the vehicle 1 (the Y-axisdirection of the vehicle body coordinate system), that is, the treadbetween the front wheels 2-1 and 2-2. A reference character “dr” denotesthe interval between the rear wheels 2-3 and 2-4 in the lateraldirection of the vehicle 1 (the Y-axis direction of the vehicle bodycoordinate system), that is, the tread between the rear wheels 2-3 and2-4. Hereinafter, “df” will stand for the front wheel tread and “dr”will stand for the rear wheel tread.

A reference character “Lf” denotes the distance between the axle(rotating shaft) of the front wheels 2-1 and 2-2 and thecenter-of-gravity point of the vehicle 1, i.e., the distance in thelongitudinal direction of the vehicle 1, when δ1=δ2=0. A referencecharacter “Lr” denotes the distance between the axle (rotating shaft) ofthe rear wheels 2-3 and 2-4 and the center-of-gravity point of thevehicle 1, i.e., the distance in the longitudinal direction of thevehicle 1. Hereinafter, Lf will stand for the distance between the axleof the front wheels and the center of gravity, while Lr will stand forthe distance between the axle of the rear wheels and the center ofgravity.

A reference character “↑Pi” denotes a position vector of the i-th wheel2-i (hereinafter referred to simply as the wheel position vector in somecases) as observed from the center-of-gravity point of the vehicle 1when the vehicle 1 is observed from above in the yaw-axis direction.Each wheel position vector ↑Pi is a vector composed of a component inthe X-axis direction and a component in the Y-axis direction of thevehicle body coordinate system. In this case, although not shown inFIGS. 2( a) and 2(b), the component in the X-axis direction of eachwheel position vector ↑Pi will be denoted by Px_i, while the componentin the Y-axis direction thereof will be denoted by Py_i.

In the case where the center-of-gravity point of the vehicle 1 in theY-axis direction of the vehicle body coordinate system lies on thecentral line of the vehicle width of the vehicle 1, ↑P1=(Lf, df/2)^(T),↑P2=(Lf, −df/2)^(T), ↑P3=(−Lr, df/2)^(T), and ↑P4=(−Lr, −dr/2)^(T) hold.

A reference character “↑Fi” denotes a road surface reaction force of thei-th wheel 2-i (a translational force vector acting from a road surfaceonto the i-th wheel 2-i), as observed by being projected onto the XYplane of the vehicle body coordinate system. Hereinafter, ↑Fi denotes awheel two-dimensional road surface reaction force or a two-dimensionalroad surface reaction force. The wheel two-dimensional road surfacereaction force ↑Fi denotes a vector composed of a component in theX-axis direction and a component in the Y-axis direction of a vehiclebody coordinate system.

Here, spatially (three-dimensionally), the road surface reaction forceacting on each wheel 2-i from a road surface is a resultant force vectorof the driving/braking force, which is a translational force componentin the x-axis direction of the i-th wheel coordinate system, a lateralforce, which is a translational force component in the y-axis directionthereof, and a ground contact load, which is a translational forcecomponent in the yaw-axis direction. Therefore, the wheeltwo-dimensional road surface reaction force ↑Fi is a vector obtained byrepresenting the resultant vector of the driving/braking force and thelateral force of the i-th wheel 2-i (corresponding to the frictionalforce acting on the i-th wheel 2-2 from a road surface) by means of thevehicle body coordinate system. In this case, although not shown inFIGS. 2( a) and 2(b), the component in the X-axis direction of the wheeltwo-dimensional road surface reaction force ↑Fi is denoted by Fx_i andthe component in the Y-axis direction thereof is denoted by Fy_i.

In the following description, the spatial road surface reaction force asthe resultant vector of the driving/braking force, the lateral force,and the ground contact load of each wheel 2-i will be referred to as thewheel three-dimensional road surface reaction force or thethree-dimensional road surface reaction force. Further, the groundcontact load, which is a component in the yaw-axis direction of thethree-dimensional road surface reaction force of each wheel 2-i, will bedenoted by Fz_i.

A reference character “↑Fsub_i” denotes the road surface reaction forceof the i-th wheel 2-i as observed by being projected onto the xy planeof the i-th wheel coordinate system (hereinafter referred to as thewheel two-dimensional road surface reaction force on the wheelcoordinate system). Each wheel two-dimensional road surface reactionforce on the wheel coordinate system ↑Fsub_i is a vector composed of acomponent in the x-axis direction of the i-th wheel coordinate systemand a component in the y-axis direction thereof.

In this case, although not shown in FIGS. 2( a) and 2(b), the componentin the x-axis direction of each wheel two-dimensional road surfacereaction force ↑Fi on the wheel coordinate system is denoted by Fsubx_iand the component in the y-axis direction thereof is denoted by Fsuby_i.The component in the x-axis direction Fsubx_i is, in other words, thedriving/braking force of the i-th wheel 2-i. The component in the y-axisdirection Fsuby_i is, in other words, the lateral force of the i-thwheel 2-i. The wheel two-dimensional road surface reaction force ↑Fsub_ion the wheel coordinate system of the i-th wheel 2-i and the wheeltwo-dimensional road surface reaction force ↑Fi of the i-th wheel 2-iare vector quantities sharing the same spatial orientation and magnitudeexcept that the coordinate systems for representing the vectorquantities are different.

A reference character “↑Fg_total” denotes a spatial translational forcevector acting on the center-of-gravity point of the vehicle 1(hereinafter referred to as the total road surface reaction forceresultant translational force vector) due to the resultant force of theroad surface reaction forces acting on the wheels 2-i (i=1, 2, 3, 4),i.e., the resultant force of the wheel three-dimensional road surfacereaction forces (i=1, 2, 3, 4).

In this case, although not shown in FIGS. 2( a) and 2(b), the componentin the X-axis direction of the vehicle body coordinate system of thetotal road surface reaction force resultant translational force vector↑Fg_total is denoted by Fgx_total, the component in the Y-axis directionthereof the vehicle body coordinate system is denoted by Fgy_total, andthe component in the yaw-axis direction is denoted by Fgz_total. Thereference character Fgx_total may be referred to as the total roadsurface reaction force resultant longitudinal force and the referencecharacter Fgy_total may be referred to as the total road surfacereaction force resultant lateral force in some cases.

A reference character “Mgz_total” denotes a moment acting about the yawaxis at the center-of-gravity point of the vehicle 1 due to theresultant force of the road surface reaction forces acting on the wheels2-i (i=1, 2, 3, 4), i.e., the resultant force of the wheelthree-dimensional road surface reaction forces (i=1, 2, 3, 4). Themoment Mgz_total will be hereinafter referred to as the total roadsurface reaction force resultant yaw moment.

The component in the yaw-axis direction Fgz_total of the resultant forceof the wheel three-dimensional road surface reaction forces (i=1, 2, 3,4) does not contribute to the total road surface reaction forceresultant yaw moment Mgz_total. Hence, the total road surface reactionforce resultant yaw moment Mgz_total virtually means the moment actingabout the yaw axis at the center-of-gravity point of the vehicle 1 dueto the resultant force of the wheel two-dimensional road surfacereaction forces ↑Fi (i=1, 2, 3, 4), i.e., the resultant force of thedriving/braking forces and the lateral forces of all wheels 2-i (i=1, 2,3, 4).

Supplementally, in each of the embodiments described in the presentspecification, the resultant force of the road surface reaction forcesacting on the wheels 2-i (i=1, 2, 3, 4) is regarded as the entireexternal force acting on the vehicle 1. More specifically, the externalforces acting on the vehicle 1 include air resistance and the like inaddition to the road surface reaction force acting on each wheel 2-ifrom a road surface. In each of the embodiments, however, externalforces other than road surface reaction forces are consideredsufficiently small to be ignored, as compared with the resultant forceof road surface reaction forces acting on the wheels 2-i (i=1, 2, 3, 4).Thus, ↑Fg_total and Mgz_total mean a translational force vector and amoment, respectively, acting on the center-of-gravity point of thevehicle 1 due to the whole external force acting on the vehicle 1.

A reference character “NSP” denotes the neutral steer point of thevehicle 1. The NSP means the load application point (the working point)of the resultant force of the lateral forces Fsuby_i (i=1, 2, 3, 4)acting on all the wheels 2-i (i=1, 2, 3, 4) when a vehicle center ofgravity side slip angle βg (≠0) occurs while the vehicle 1 is travelingin a situation wherein δ1=δ2=0 holds.

More specifically, the NSP means an intersecting point of the straightline which passes the center-of-gravity point of the vehicle 1 andextends in the X-axis direction of the vehicle body coordinate system(the longitudinal direction of the vehicle 1) and the line of action ofthe resultant force of the lateral forces Fsuby_i (i=1, 2, 3, 4) actingon all wheels 2-i (i=1, 2, 3, 4) when the vehicle 1 is observed fromabove in the yaw-axis direction.

A reference character “Lnsp” denotes the distance between thecenter-of-gravity point of the vehicle 1 in the X-axis direction of thevehicle body coordinate system (the longitudinal direction of thevehicle 1) and the NSP (hereinafter referred to as the distance betweenthe vehicle center of gravity and the NSP).

If the NSP lies on a rear side beyond the center-of-gravity point of thevehicle 1, then a value of the distance Lnsp between the vehicle centerof gravity and the NSP will be a positive value. If the NSP lies on afront side beyond the center-of-gravity point of the vehicle 1, then avalue of the distance Lnsp between the vehicle center of gravity and theNSP will be a negative value.

A reference character “Mnsp” denotes a moment acting about the yaw axisat the NSP (hereinafter referred to as the NSP yaw moment) due to theresultant force of the road surface reaction forces acting on the wheels2-i (i=1, 2, 3, 4), that is, the resultant force of the wheelthree-dimensional road surface reaction forces (i=1, 2, 3, 4) or theresultant force of the wheel two-dimensional road surface reactionforces ↑Fi (i=1, 2, 3, 4).

In other words, the NSP yaw moment Mnsp is a moment of the sum of thetotal support force reaction force resultant yaw moment Mgz_total andthe moment generated about the yaw axis at the NSP by the total roadsurface reaction force resultant translational force vector ↑Fg_total(=Lnsp*Fgy_total).

Supplementally, in each of the embodiments, regarding the state amountsrelated to a rotational motion about the yaw axis, such as an angleabout the yaw axis, an angular velocity, and angular acceleration (δi,βi, and γ), and the moments about the yaw axis (Mgz_total, Mnsp and thelike), a counterclockwise direction is defined as a positive directionwhen the vehicle 1 is observed from above in the yaw-axis direction.

Although not shown in FIGS. 2( a) and 2(b), variables given below willbe used in the following description in addition to the aforesaidvariables (reference characters).

A reference character “θh” denotes the steering angle of the steeringwheel 5 (a rotational angle, which will be referred to as the steeringcontrol angle).

A reference character “γdot” denotes the angular acceleration about theyaw axis of the vehicle 1 (hereinafter referred to as the yaw angularacceleration).

A reference character “ωw_i” denotes the rotational angular velocity ofthe i-th wheel 2-i (hereinafter referred to simply as the wheelrotational angular velocity in some case). A reference character “Rw_i”denotes the effective radius of the i-th wheel 2-i (hereinafter referredto simply as the wheel effective radius). A reference character “Vw_i”denotes the wheel velocity of the i-th wheel 2-i defined as the productof ωw_i and Rw_i (=ωw_i*Rw_i), i.e., the velocity of the ground contactportion of the i-th wheel 2-i in the circumferential direction, asobserved from the center of the rotation of the i-th wheel 2-i.

Each wheel velocity Vw_i coincides with the component in the x-axisdirection Vsubx_i of the wheel advancing speed vector on the wheelcoordinate system ↑Vsub_i in a state wherein no slip of the i-th wheel2-i exists.

A reference character “κi” denotes the slip rate of the i-th wheel 2-i(a longitudinal slip rate: hereinafter referred to simply as the wheelslip rate in some cases). A reference character “Tq_i” denotes a torqueof the sum of a driving torque supplied from the drive system of thevehicle 1 to the i-th wheel 2-i and a braking torque supplied from thebraking system of the vehicle 1 (hereinafter referred to simply as thewheel torque in some cases). A reference character “Iw_i” denotes theinertial moment of the i-th wheel 2-i (hereinafter referred to simply asthe wheel inertial moment in some cases).

A reference character “m” denotes the mass of the entire vehicle 1(hereinafter referred to as the vehicle mass), and a reference character“Iz” denotes the inertial moment about the yaw axis of the entirevehicle 1 (hereinafter referred to as the vehicle yaw inertial moment).

A reference character “Accx” denotes the acceleration (Vgdot_x−Vgy*γ)obtained by adding the component in the X-axis direction of the vehiclebody coordinate system of the acceleration (=−Vgy*γ) produced at thecenter-of-gravity point of the vehicle 1 due to a centrifugal force froma turning motion of the vehicle 1 to the vehicle center of gravitylongitudinal velocity change rate Vgdot_x (=Vgdot_x−Vgy*γ).

A reference character “Accy” denotes the acceleration (Vgdot_y+Vgx*γ)obtained by adding the component in the Y-axis direction of the vehiclebody coordinate system of the acceleration (=Vgx*γ) produced at thecenter-of-gravity point of the vehicle 1 due to a centrifugal force froma turning motion of the vehicle 1 to the vehicle center of gravity sideslip velocity change rate Vgdot_y (=Vgdot_y+Vgx*γ).

In other words, the Accx and the Accy denote the component in the X-axisdirection and the component in the Y-axis direction, respectively, ofthe acceleration of a motion of the center-of-gravity point of thevehicle 1 observed in the vehicle body coordinate system (a second orderdifferential value of the position of the center-of-gravity point in thevehicle body coordinate system). Hereinafter, the Accx will be referredto as the longitudinal vehicle center of gravity acceleration and theAccy will be referred to as the lateral vehicle center of gravityacceleration.

A reference character “μ” denotes the frictional coefficient of a roadsurface (the coefficient of friction relative to each wheel 2-i:hereinafter referred to as the road surface frictional coefficient insome cases).

The road surface frictional coefficient μ in each of the embodiments isa relative frictional coefficient which uses, as the reference thereof,the coefficient of friction between a road surface in a certainreference state, such as a standard dry road surface (hereinafterreferred to as the reference road surface) and each wheel 2-i. The roadsurface frictional coefficient μ is to be considered the same at aground contact location of any one of the wheels 2-i (i=1, 2, 3, 4).

A reference character “θbank” denotes the bank angle of a road surface(hereinafter referred to as the road surface bank angle in some cases).A reference character “θslope” denotes a slope angle of a road surface(hereinafter referred to as the road surface slope angle in some cases).The road surface bank angle θbank is the inclination angle of a roadsurface relative to a horizontal plane, as observed in the direction ofthe roll axis of the vehicle 1. The road surface slope angle θslope isthe inclination angle of a road surface relative to a horizontal plane,as observed in the direction of the pitch axis of the vehicle 1.

The road surface bank angle θbank is generally referred to as a cantangle of a road surface in an automotive engineering field. In thepresent specification, however, the term “bank angle” will be used. Ineach of the embodiments described in the present specification, a roadsurface bank angle θbank in the case where the vehicle 1 on a roadsurface is in a right-down sloping posture is defined as a positiveangle. Further, a road surface slope angle θslope in the case where thevehicle 1 on a road surface is in a front-down sloping posture isdefined as a positive angle.

A reference character “Rot(δi)” denotes a coordinate conversion matrixfor converting a vector quantity expressed in terms of the i-th wheelcoordinate system (a vector quantity formed of a component in the x-axisdirection and a component in the y-axis direction of the i-th wheelcoordinate system) into a vector quantity expressed in terms of thevehicle body coordinate system (a vector quantity formed of a componentin the X-axis direction and a component in the Y-axis direction of thevehicle body coordinate system). A coordinate conversion matrix R(δi) isa matrix (secondary square matrix) which is dependant on the steeringangle δi of the i-th wheel 2-i and which has row vectors (cos(δi),sin(δi))^(T) and (−sin(δi), cos(δi))^(T) as a component of a firstcolumn and a component of a second column, respectively. In this case,if a certain vector quantity ↑A is denoted by (ax, ay)^(T) on the i-thwheel coordinate system and denoted by (Ax, Ay)^(T) on the vehicle bodycoordinate system, then the relationship between (Ax, Ay)^(T) and (ax,ay)^(T) is expressed by (Ax, Ay)^(T)=Rot(δi)*(ax, ay)^(T). Accordingly,the relationship between the wheel advancing speed vector ↑Vi of each ofthe wheels 2-i and the wheel advancing speed vector on the wheelcoordinate system ↑Vsub_i is given by ↑Vi=Rot(δi)*↑Vsub_i.

Similarly, the relationship between the wheel two-dimensional roadsurface reaction force ↑Fi of each of the wheels 2-i and the wheeltwo-dimensional road surface reaction force ↑Fsub_i on the wheelcoordinate system is given by ↑Fi=Rot(δi)*↑Fsub_i. The coordinateconversion matrix for converting a vector quantity expressed on thevehicle body coordinate system into a vector quantity expressed on thei-th wheel coordinate system, i.e., an inversed matrix of Rot(δi), willbe Rot(−δi).

In the following description, the term “actual” will, in some cases,prefix a name or a designation, such as a state amount or a vectorquantity, like “an actual yaw rate” to represent the state amount or thevector quantity of an actual value (true value). In this case, avariable (reference character) denoting the state amount or the vectorquantity will be suffixed by “_act” (e.g., “γ_act”).

Further, to express an observed value (a detected value or an estimatedvalue) of a state amount or a vector quantity, the name (designation) ofthe state amount or the vector quantity will be suffixed by “detectedvalue” or “estimated value” (e.g., “yaw rate detected value” or “yawrate estimated value”). In this case, as a general rule, the term“estimated value” will be used for other observed values generated onthe basis of observed values calculated by a vehicle model calculator24, which will be described later, or on the basis of the calculatedobserved values.

Further, the term “detected value” will be used for an observed valuewhich is obtained on the basis of an output of a certain sensor withoutusing the observed value calculated by the vehicle model calculator 24.For a detected value, a variable (reference character) will be suffixedby “_sens” (e.g., “γ_sens”). For an estimated value, a variable(reference character) will be suffixed by “_estm” (e.g., “γ_estm”).

Further, to express a temporal change rate of a state amount (adifferential value based on time), “dot” will be added in a variable(reference character) of a state amount (e.g., “γdot”).

Based on the description given above, the embodiments of the presentinvention will be described in detail.

First Embodiment

First, the processing by the controller 20 in a first embodiment will bedescribed in detail. In the present embodiment, as illustrated by theblock diagram of FIG. 3, the controller 20 has, as major functionalmeans, an amount-to-be-observed detector 22, a vehicle model calculator24, a μ estimator 26, a bank angle estimator 28, and a slope angleestimator 30.

The amount-to-be-observed detector 22 uses outputs from the aforesaidvarious sensors of the vehicle 1 (detection data) to carry out theprocessing for detecting predetermined types of amounts to be observedrelated to a behavior of the vehicle 1, and generates detected values ofthe amounts to be observed.

In the present embodiment, the amounts to be observed by theamount-to-be observed detector 22 include actual steering angles δ1_actand δ2_act of steering control wheels (front wheels) 2-1 and 2-2, anactual wheel speed Vw_i_act (i=1, 2, 3, 4), an actual yaw rate γ_act andan actual yaw angular acceleration γdot_act of the vehicle 1, an actualvehicle center of gravity longitudinal acceleration Accx_act and anactual vehicle center of gravity lateral acceleration Accy_act, and anactual wheel torque Tq_i_act (i=1, 2, 3, 4).

To generate the detected values of the amounts to be observed, theamount-to-be-observed detector 22 has a wheel steering angle detector 22a which generates wheel steering angle detected values δ1_sens andδ2_sens of the front wheels 2-1 and 2-2, respectively, a wheel speeddetector 22 b which generates the wheel speed detected value Vw_i_sens(i=1, 2, 3, 4), a yaw rate detector 22 c which generates a yaw ratedetected value γ_sens, a yaw angular acceleration detector 22 d whichgenerates a yaw angle acceleration detected value γdot_sens, alongitudinal acceleration detector 22 e which generates the vehiclecenter of gravity longitudinal acceleration detected value Accx_sens, alateral acceleration detector 22 f which generates the vehicle center ofgravity lateral acceleration detected value Accy_sens, and a wheeltorque detector 22 g which generates a wheel torque detected valueTq_i_sens (i=1, 2, 3, 4).

The vehicle model calculator 24 estimates a road surface reaction forceacting on each wheel 2-i by using a dynamic model, which includes afriction characteristic model which expresses a relationship between theslip between each wheel 2-i and a road surface and a road surfacereaction force acting on the wheel 2-i from the road surface and avehicle motion model which expresses a relationship between an externalforce acting on the vehicle 1 and a motion of the vehicle 1 (hereinafterreferred to simply as the vehicle model in some cases). The vehiclemodel calculator 24 also carries out the processing for estimating thestate amount of a motion of the vehicle 1 dynamically caused by the roadsurface reaction force acting as the external force on the vehicle 1.

To carry out the processing, the vehicle model calculator 24 receivesthe detected values of the predetermined types of amounts to be observed(in the present embodiment, δ1_sens, δ2_sens, Vw_i_sens, γ_sens,Accx_sens, Accy_sens, and Tq_i_sens) and also a latest road surfacefrictional coefficient estimated value μ_estm which has already beendetermined by the μ estimator 26. Then, the vehicle model calculator 24uses these received values and the aforesaid vehicle model to estimatethe road surface reaction force of each wheel 2-i or the state amountsof the motion of the vehicle 1.

The estimated values determined by the vehicle model calculator 24 areroughly classified into a road surface reaction force estimated value,which is an estimated value related to a road surface reaction force,the translational motions in the longitudinal direction (the directionof the roll axis) and a lateral direction (the direction in the pitchaxis) of the vehicle 1, and a vehicle motional state amount estimatedvalue, which is the estimated value of a state amount related to arotational motion about the yaw axis.

In this case, the road surface reaction force estimated value includesthe driving/braking force Fsubx_i of each wheel 2-i, the lateral forceFusby_i, and a ground contact load Fz_i, and also includes a total roadsurface reaction force combined translational force vector estimatedvalue ↑Fg_total_estm (Fgx_total_estm and Fgy_total_estm), and the totalroad surface reaction force resultant yaw moment estimated valueMgz_total_estm.

Further, the vehicle motional state amount estimated value includes theyaw rate estimated value γ_estm, the vehicle center of gravity velocityvector estimated value ↑Vg_estm (Vgx_estm and Vgy_estm), the vehiclecenter of gravity longitudinal acceleration estimated value Accx_estm,and the vehicle center of gravity lateral acceleration estimated valueAccy_estm.

The μ estimator 26 carries out the processing for estimating thefrictional coefficient μ of a road surface on which the vehicle 1 istraveling (the road surface frictional coefficient μ).

To implement the processing, the μ estimator 26 receives δ1_sens,δ2_sens, γ_sens, γdot_sens, and Accy_sens among the detected values ofthe amounts to be observed which have been generated by theamount-to-be-observed detector 22, the total road surface reaction forceresultant translational force vector estimated value ↑Vg_total_estm(more specifically, the total road surface reaction force resultantlateral force estimated value Fgy_total_estm of ↑Vg_total_estm) and thetotal road surface reaction force resultant yaw moment estimated valueMgz_total_estm calculated by the vehicle model calculator 24, and thevehicle center of gravity longitudinal velocity estimated valueVgx_estm, which is the component in the X-axis direction (the componentin the longitudinal direction of the vehicle 1) of the vehicle center ofgravity velocity vector estimated value ↑Vg_estm of the vehicle motionalstate amount estimated value calculated by the vehicle model calculator24. Then, the μ estimator 26 uses these input values to calculate theroad surface frictional coefficient estimated value μ_estm, which is theestimated value of the road surface frictional coefficient μ.

The bank angle estimator 28 carries out the processing for estimatingthe road surface bank angle θbank (the bank angle θbank of a roadsurface on which the vehicle 1 is traveling).

To carry out the processing, the bank angle estimator 28 receives thevehicle center of gravity lateral acceleration detected value Accy_sensof the detected values of the amounts to be observed that have beengenerated by the amount-to-be-observed detector 22 and the vehiclecenter of gravity lateral acceleration estimated value Accy_estm of thevehicle motional state amount estimated values calculated by the vehiclemodel calculator 24. Then, the bank angle estimator 28 uses the inputvalues to calculate the road surface bank angle estimated valueθbank_estm, which is the estimated value of the bank angle θbank of theroad surface.

The slope angle estimator 30 carries out the processing for estimatingthe road surface slope angle θslope (the slope angle θslope of a roadsurface on which the vehicle 1 is traveling).

To carry out the processing, the slope angle estimator 30 receives thevehicle center of gravity longitudinal acceleration detected valueAccx_sens of the detected values of the amounts to be observed that havebeen generated by the amount-to-be-observed detector 22 and the vehiclecenter of gravity acceleration estimated value Accx_estm of the vehiclemotional state amount estimated values calculated by the vehicle modelcalculator 24. Then, the slope angle estimator 30 uses the input valuesto calculate the road surface slope angle estimated value θslope_estm,which is the estimated value of the road surface slope angle θslope.

The controller 20 sequentially implements the processing illustrated bythe flowchart of FIG. 4 at a predetermined arithmetic processing cycleby the amount-to-be-observed detector 22, the vehicle model calculator24, the μ estimator 26, the bank angle estimator 28, and the slope angleestimator 30.

In the following description, in order to distinguish the value (adetected value, an estimated value, or the like) obtained in the current(present) arithmetic processing cycle of the controller 20 from a valueobtained in the previous (last) arithmetic processing cycle, the formerwill be referred to as “the current value” and the latter as “theprevious value” in some cases. Further, the reference character of theprevious value will be suffixed by a subscript “_p” (e.g., “γ_estm_p”).In this case, “the previous value” means the latest value among thevalues already obtained in past arithmetic processing cycles of thecontroller 20. Any value will mean a current value unless otherwisespecified as a current value or a previous value.

Referring to FIG. 4, the controller 20 first carries out the processingby the amount-to-be-observed detector 22 in S100. Theamount-to-be-observed detector 22 generates the detected values δ1_sens,δ2_sens, Vw_i_sens (i=1, 2, 3, 4), γ_sens, γdot_sens, Accx_sens,Accy_sens, and Tq_i_sens of the amounts to be observed on the basis ofthe outputs of various sensors, including the wheel rotational angularvelocity sensor 8-i (i=1, 2, 3, 4), a brake pressure sensor 9-i (i=1, 2,3, 4), the steering control angle sensor 10, the transmission sensor 11,the accelerator (gas) pedal sensor 12, the yaw rate sensor 13, thelongitudinal acceleration sensor 14, and the lateral acceleration sensor15.

More specifically, the wheel steering angle detected values δ1_sens andδ2_sens are generated by the wheel steering angle detector 22 a on thebasis of outputs of the steering control angle sensor 10. Here, in thepresent embodiment, the actual steering angle δ1_act of the first wheel2-1 and the actual steering angle δ2_act of the second wheel 2-2 are thesame, so that the δ1_sens is regarded as equal to δ2_sens. Accordingly,hereinafter, the steering angles δ1 and δ2 of the front wheels 2-1 and2-2 will be generically referred to as a front steering angle δf, andthe wheel steering angle detected values δ1_sens and δ2_sens will begenerically referred to as a front wheel steering angle detected valueδf_sens.

Then, the wheel steering angle detector 22 a determines the front wheelsteering angle detected value δf_sens (=δ1_sens=δ2_sens) as the steeringangle detected value common to the front wheels 2-1 and 2-2 on the basisof a steering control angle detected value θh_sens, which is the valueof a steering control angle (converted value) indicated by an outputvalue of the steering control angle sensor 10, according to a presetrelationship (in the form of a model, a map or the like) between thesteering control angle θh and the front wheel steering angle δf.

For example, in the case where the steering mechanism of the vehicle 1is constructed such that the actual steering angles δ1_act and δ2_act ofthe front wheels 2-1 and 2-2 are substantially proportional to theactual steering control angle θh_act, the δf_sens is calculated bymultiplying the θh_sens by a preset proportional constant, which is theso-called overall steering ratio.

In the case where the steering mechanism of the steering system has asteering actuator, as with a power steering, the operation state of thesteering actuator or a state amount defining the operation state may bedetected in addition to the steering control angle detected valueθh_sens or in place of the steering control angle detected value θh_sensand the detected value may be used to determine the front wheel steeringangle detected value δf_sens.

Alternatively, a more accurate steering system model or the like may beused to separately determine the steering angle detected values δ1_sensand δ2_sens of the front wheels 2-1 and 2-2, respectively. Then, theaverage value of the individual steering angle detected values δ1_sensand δ2_sens of the front wheels 2-1 and 2-2 (=(δ1_sens+δ2_sens)/2) maybe determined as the front wheel state amount detected value of δf_sensthat represents the actual steering angles δ1_act and δ2_act of thefront wheels 2-1 and 2-2.

The wheel speed detected values Vw_i_sens (i=1, 2, 3, 4) are generatedby the wheel speed detector 22 b on the basis of the outputs of thewheel rotational angular velocity sensors 8-i respectively correspondingthereto.

To be more specific, the wheel speed detector 22 b determines the wheelspeed detected value Vw_i_sens by multiplying the wheel rotationalangular velocity detected value ωw_i_sens, which is the value of angularacceleration (converted value) indicated by an output value of the wheelrotational angular velocity sensor 8-i, by the value of a preseteffective radius Rw_i of the i-th wheel 2-i for each wheel 2-i.

The yaw rate detected value γ_sens and the yaw angular accelerationdetected value γdot_sens are generated by the yaw rate detector 22 c andthe yaw angular acceleration detector 22 d, respectively, on the basisof the outputs of the yaw rate sensor 13.

More specifically, the yaw rate detector 22 c generates the value(converted value) of the angular velocity, which is indicated by anoutput value of the yaw rate sensor 13, as the yaw rate detected valueγ_sens.

The yaw angular acceleration detector 22 d differentiates the yaw ratedetected value γ_sens, i.e., determines a temporal change rate togenerate the yaw angular acceleration detected value γdot_sens, orgenerates the value (converted value) of the angular acceleration, whichis indicated by the value obtained by differentiating an output value ofthe yaw rate sensor 13, as the yaw angular acceleration detected valueγdot_sens.

Alternatively, the yaw angular acceleration detected value γdot_sens canbe generated on the basis of an output of a different sensor from theyaw rate sensor 13. For instance, two acceleration sensors may beinstalled in the vehicle body 1B such that the sensors are spaced awayfrom each other with an interval Lacc provided therebetween in thedirection orthogonal to the direction of the yaw axis of the vehicle 1(e.g., in the direction of the roll axis or the pitch axis of thevehicle 1).

In this case, these two acceleration sensors are disposed such that thetwo acceleration sensors sense the acceleration in a directionorthogonal to the direction of the interval between the two accelerationsensors and to the direction of the yaw axis. This arrangement allowsthe yaw angular acceleration detected value γdot_sens to be generated bydividing the difference between the acceleration detected valuesindicated by the output values of the two acceleration sensors by theinterval Lacc.

The vehicle center of gravity longitudinal acceleration detected valueAccx_sens is generated by the longitudinal acceleration detector 22 e onthe basis of an output of the longitudinal acceleration sensor 14.Further, the vehicle center of gravity lateral acceleration detectedvalue Accy_sens is generated by the lateral acceleration detector 22 fon the basis of an output of the lateral acceleration sensor 15.

Here, in the present embodiment, the position of the center-of-gravitypoint of the vehicle 1 is identified beforehand, and the longitudinalacceleration sensor 14 and the lateral acceleration sensor 15 are fixedto the vehicle body 1B such that the sensors are positioned at thecenter-of-gravity point. The longitudinal acceleration sensor 14 and thelateral acceleration sensor 15 may be an acceleration sensor combiningthe two sensors into one, i.e., a two-axis acceleration sensor.

The longitudinal acceleration detector 22 e generates the value(converted value) of the acceleration indicated by an output value ofthe longitudinal acceleration sensor 14 as the vehicle center of gravitylongitudinal acceleration detected value Accx_sens. The lateralacceleration detector 22 f generates the value (converted value) of theacceleration indicated by an output value of the lateral accelerationsensor 15 as the vehicle center of gravity lateral acceleration detectedvalue Accy_sens.

Even if the longitudinal acceleration sensor 14 or the lateralacceleration sensor 15 is disposed at a position deviating from thecenter-of-gravity point of the vehicle 1, the vehicle center of gravitylongitudinal acceleration detected value Accx_sens or the vehicle centerof gravity lateral acceleration detected value Accy_sens can begenerated by correcting the acceleration detected value indicated by anoutput value of the sensor 14 or 15 according to the yaw angularacceleration detected value γdot_sens (or the differential value of theyaw rate detected value γ_sens).

For example, if the longitudinal acceleration sensor 14 is disposed at aposition which is away to the left side from the center-of-gravity pointof the vehicle 1 by an interval denoted by Ly, then the vehicle centerof gravity longitudinal acceleration detected value Accx_sens can begenerated by adding the value, which is obtained by multiplying the yawangular acceleration detected value γdot_sens (or the differential valueof the yaw rate detected value γ_sens) by Ly, to the accelerationdetected value indicated by an output value of the longitudinalacceleration sensor 14 (the detected value of the acceleration at theposition of the sensor 14).

Similarly, if the lateral acceleration sensor 15 is disposed at aposition which is away to the front side from the center-of-gravitypoint of the vehicle 1 by an interval denoted by Lx, then the vehiclecenter of gravity lateral acceleration detected value Accy_sens can begenerated by subtracting the value obtained by multiplying the yawangular acceleration detected value γdot_sens (or the differential valueof the yaw rate detected value γ_sens) by Lx from the accelerationdetected value indicated by an output value of the lateral accelerationsensor 15 (the detected value of the acceleration at the position of thesensor 15).

Supplementally, the acceleration detected or sensed by the longitudinalacceleration sensor 14 carries a meaning as the component in thelongitudinal direction of the vehicle body 1B (the component in theX-axis direction of the vehicle body coordinate system) of anacceleration vector generated at the center-of-gravity point of thevehicle 1 by the entire external force (resultant force) acting on thevehicle 1 (the acceleration vector obtained by dividing thetranslational force vector acting on the center-of-gravity point of thevehicle 1 due to the entire external force by a vehicle 1 mass m).

In this case, if the actual road surface slope angle θslope_act is zero,then the acceleration sensed by the longitudinal acceleration sensor 14will be the actual vehicle center of gravity longitudinal accelerationAccx_act itself as the proper object to be detected. Meanwhile, if theactual road surface slope angle θslope_act is not zero, then thelongitudinal direction (the X-axis direction) of the vehicle body 1B,which is the sensing direction of the longitudinal acceleration sensor14, will be inclined by θslope_act relative to a horizontal plane.

Hence, the longitudinal acceleration sensor 14 senses not only theactual vehicle center of gravity longitudinal acceleration Accx_act butalso an acceleration component in a direction parallel to thelongitudinal direction of the vehicle body 1B (=−g*sin(θslope_act); g:Gravitational acceleration constant) of the gravitational acceleration.

Thus, the vehicle center of gravity longitudinal acceleration detectedvalue Accx_sens as the acceleration indicated by an output of thelongitudinal acceleration sensor 14 will be actually the detected valueof the acceleration obtained by superimposing an acceleration componentin a direction parallel to the longitudinal direction of the vehiclebody 1B of the gravitational acceleration onto the actual vehicle centerof gravity longitudinal acceleration Accx_act(=Accx_act−g*sin(θslope_act)). This includes the case where θslope_actis zero.

Similarly, the acceleration detected or sensed by the lateralacceleration sensor 15 carries a meaning as the component in the lateraldirection of the vehicle body 1B (the component in the Y-axis directionof the vehicle body coordinate system) of an acceleration vectorgenerated at the center-of-gravity point of the vehicle 1 by the entireexternal force (resultant force) acting on the vehicle 1. In this case,if the actual road surface bank angle θbank_act is zero, then theacceleration sensed by the lateral acceleration sensor 15 will be theactual vehicle center of gravity lateral acceleration Accy_act itself asthe proper object to be detected.

Meanwhile, if the actual road surface bank angle θbank_act is not zero,then the lateral direction (the Y-axis direction) of the vehicle body1B, which is the sensing direction of the lateral acceleration sensor15, will be inclined by θbank_act relative to a horizontal plane. Hence,the lateral acceleration sensor 15 senses not only the actual vehiclecenter of gravity lateral acceleration Accy_act but also an accelerationcomponent in a direction parallel to the lateral direction of thevehicle body 1B (=g*sin(θbank_act)).

Thus, the vehicle center of gravity lateral acceleration detected valueAccy_sens as the acceleration indicated by an output of the lateralacceleration sensor 15 will be actually the detected value of theacceleration obtained by superimposing an acceleration component in adirection parallel to the lateral direction of the vehicle body 1B ofthe gravitational acceleration onto the actual vehicle center of gravitylateral acceleration Accy_act (=Accy_act+g*sin(θbank_act)). Thisincludes the case where θbank_act is zero.

In the following description, the acceleration defined as the sum of thevehicle center of gravity longitudinal acceleration Accx and theacceleration component in the direction parallel to the longitudinaldirection of the vehicle body 1B (=−g*sin(θslope)) of the gravitationalacceleration (=Accx−g*sin(θslope)), that is, the acceleration sensed bythe longitudinal acceleration sensor 14, will be referred to as thesensed-by-sensor longitudinal acceleration Accx_sensor.

Similarly, the acceleration defined as the sum of the vehicle center ofgravity lateral acceleration Accy and the acceleration component in thedirection parallel to the lateral direction of the vehicle body 1B(=g*sin(θbank)) of the gravitational acceleration (=Accx+g*sin(θbank)),that is, the acceleration sensed by the lateral acceleration sensor 15,will be referred to as the sensed-by-sensor lateral accelerationAccy_sensor.

The sensed-by-sensor longitudinal acceleration Accx_sensor agrees withthe vehicle center of gravity longitudinal acceleration Accx when θslopeis zero. The sensed-by-sensor lateral acceleration Accy_sensor agreeswith the vehicle center of gravity lateral acceleration Accy when θbankis zero. In a precise sense, therefore, the vehicle center of gravitylongitudinal acceleration detected value Accx_sens generated by thelongitudinal acceleration detector 22 e and the vehicle center ofgravity lateral acceleration detected value Accy_sens generated by thelateral acceleration detector 22 f mean the detected value of thesensed-by-sensor longitudinal acceleration Accx_sensor and the detectedvalue the sensed-by-sensor lateral acceleration Accy_sensor,respectively.

The wheel torque detected value Tq_i_sens (i=1, 2, 3, 4) is generated bythe wheel torque detector 22 g on the basis of an output of the brakepressure sensor 9-i and outputs of the accelerator (gas) pedal sensor 12and the transmission sensor 11 corresponding thereto.

To be specific, the wheel torque detector 22 g recognizes an outputtorque (required torque) of the engine 3 from the detected value of theamount of depression on the accelerator (gas) pedal indicated by anoutput value of the accelerator (gas) pedal sensor 12 and alsorecognizes the deceleration ratio between the engine 3 and each wheel2-i from the detected value of the transmission gear ratio of thetransmission 4 a indicated by an output value of the transmission sensor11.

Then, the wheel torque detector 22 g determines the driving torque to betransmitted to each wheel 2-i from the engine 3 (the driving torque tobe imparted to each wheel 2-i by the drive system of the vehicle 1) onthe basis of the recognized output torque of the engine 3 and theaforesaid deceleration ratio.

Further, the wheel torque detector 22 g determines the braking torque tobe imparted to each wheel 2-i from each braking mechanism 7-i (thebraking torque to be imparted to each wheel 2-i by the braking system ofthe vehicle 1) on the basis of the brake pressure detected valueindicated by an output value of the brake pressure sensor 9-i.

Then, the wheel torque detector 22 g calculates the value of a torque ofthe total sum of the determined driving torque and braking torque (aresultant torque) as the wheel torque detected value Tq_i_sens for eachwheel 2-i.

The above has described the details of the processing in S100, i.e., theprocessing by the amount-to-be-observed detector 22.

In the processing by the amount-to-be-observed detector 22, an output ofa sensor may be passed through a filter, such as a high-cut filter, forremoving a high-frequency noise component and then input to thedetectors 22 a to 22 g.

Alternatively, the detected value of an amount to be observed which hasbeen obtained by using an output of a sensor as it is may be taken as aprovisional detected value, and the provisional detected value may bepassed through a filter, such as a high-cut filter, to generate a formaldetected value of the amount to be observed.

Regarding the vehicle center of gravity lateral acceleration detectedvalue Accy, in particular, if a device for detecting or estimating theroll angle of the vehicle body 1B (a relative inclination angle aboutthe roll axis of the vehicle body 1B with respect to a road surface) isprovided, then the vehicle center of gravity lateral accelerationdetected value Accy is preferably obtained as described below. Thedevice for detecting or estimating the roll angle of the vehicle body 1Bis, for example, a device which detects the stroke of a suspension by asensor and calculates the roll angle of the vehicle body 1B from thedetected value thereof.

An influence portion of an output of the lateral acceleration sensor 15attributable to a roll motion of the vehicle body 1B (an influenceportion of the gravitational acceleration contained in an output of theacceleration sensor 15 caused by the tilting of the lateral accelerationsensor 15 by a roll angle of the vehicle body 1B) is estimated by usingan observed value of the roll angle. Then, preferably, the estimatedinfluence portion is subtracted from the acceleration detected valueindicated by an output value of the lateral acceleration sensor 15 so asto obtain the vehicle center of gravity lateral acceleration detectedvalue Accy.

After carrying out the processing by the amount-to-be-observed detector22 as described above, the controller 20 carries out the processing fromS102 to S116 by the vehicle model calculator 24.

The following will explain the processing in detail with reference toFIG. 4 and FIG. 5.

As illustrated in FIG. 5, the vehicle model calculator 24 has, as thefunctions thereof, a wheel ground contact load estimator 24 a whichdetermines a ground contact load estimated value Fz_i_estm of each wheel2-i, a wheel frictional force estimator 24 b which determines adriving/braking force estimated value Fsubx_i_estm, which is theestimated value of a component in the x-axis direction of the wheeltwo-dimensional road surface reaction force ↑Fsub_i on the wheelcoordinate system of each wheel 2-i and a lateral force estimated valueFsuby_i_estm, which is the estimated value of a component in the y-axisdirection thereof, a resultant force calculator 24 c which determinesthe total road surface reaction force resultant translational forcevector ↑Fg_total_estm and the total road surface reaction forceresultant yaw moment Mgz_total_estm, a vehicle motion estimator 24 dwhich determines a vehicle motional state amount estimated value, awheel advancing speed vector estimator 24 e which determines the wheeladvancing speed vector estimated value ↑Vi_estm of each wheel 2-i, awheel motion estimator 24 f which determines the wheel speed estimatedvalue Vw_i_estm of each wheel 2-i, a wheel side slip angle estimator 24g which determines a wheel side slip angle estimated value βi estm, anda wheel slip rate estimator 24 h which determines the wheel slip rateestimated value κi_estm of each wheel 2-i.

In the processing from S102 to S116, first, in S102, the wheel groundcontact load estimator 24 a calculates the ground contact load estimatedvalue Fz_i_estm of each wheel 2-i.

In this case, according to the present embodiment, the wheel groundcontact load estimator 24 a uses the vehicle center of gravitylongitudinal acceleration detected value Accx_sens and the vehiclecenter of gravity lateral acceleration detected value Accy_sens of thedetected value of an amount to be observed, which has been obtained inS100, to calculate the ground contact load estimated value Fz_i_estm(i=1, 2, 3, 4) according to an expression 1-1 given below.

Fz _(—) i_estm=Fz0_(—) i+Wx _(—) i*Accx _(—) sens+Wy _(—) j*Accy _(—)sens   Expression 1-1

Here, in expression 1-1, Fz0 _(—) i denotes a value of the groundcontact load Fz_i of the i-th wheel 2-i in a state wherein the vehicle 1is parked (stationary) on a horizontal road surface (hereinafterreferred to as the ground contact load reference value), Wx_i denotes aweighting factor which defines a change in the ground contact load Fz_iof the i-th wheel 2-i dependent upon the vehicle center of gravitylongitudinal acceleration Accx (a change from Fz0 _(—) i), and Wy_idenotes a weighting factor which defines a change in the ground contactload Fz_i of the i-th wheel 2-i dependent upon the vehicle center ofgravity lateral acceleration Accy (a change from Fz0_i). The values ofthese Fz0_i, Wx_i, and Wy_i are predetermined values that have been setbeforehand.

Thus, according to expression 1-1, a change in the ground contact loadFz_i (an increased or decreased amount from the ground contact loadreference value Fz0_i) of each wheel 2-i attributable to theacceleration of the center-of-gravity point of the vehicle 1 (theacceleration in a direction orthogonal to the yaw-axis direction) isdetermined by linearly coupling the vehicle center of gravitylongitudinal acceleration detected value Accx_sens and the vehiclecenter of gravity lateral acceleration detected value Accy_sens. Then,the determined change is added to the ground contact load referencevalue Fz0_i to obtain the ground contact load estimated value Fz_i_estm.

Alternatively, the relationship between the vehicle center of gravitylongitudinal acceleration Accx and the vehicle center of gravity lateralacceleration Accy and the ground contact load Fz_i may be formed into amap beforehand, and the ground contact load estimated value Fz_i_estm ofeach wheel 2-i may be determined according to the map.

The Fz_i_estm may be determined by reflecting the dynamic characteristicof a suspension device (not shown) of the vehicle 1.

For example, the dynamic characteristic of the suspension device of thevehicle 1 is modeled in association with a rotational motion about theroll axis of the vehicle body 1B (a roll motion) or a rotational motionabout the pitch axis thereof (a pitch motion) in advance. Then, motionalstate amounts related to the roll motion or the pitch motion, e.g., theinclination angle of the vehicle body 1B about the roll axis or theobserved value of the changing velocity thereof, and the inclinationangle of the vehicle body 1B about the pitch axis or the observed valueof the changing velocity thereof, and the aforesaid model indicating thedynamic characteristic of the suspension device are used to estimate thetranslational force in the vertical direction, i.e., the yaw-axisdirection, acting on each wheel 2-i from the suspension device.

Then, for each wheel 2-i, the estimated translational force and thegravity acting on the wheel 2-i are added to determine the groundcontact load estimated value Fz_i_estm. This makes it possible tofurther enhance the accuracy of the ground contact load estimated valueFz_i_estm (i=1, 2, 3, 4).

If the change in the ground contact load Fz_i of each wheel 2-i isregarded sufficiently small, then the processing in S102 may be omittedand the ground contact load estimated value Fz_i_estm may be set to apredetermined value that has been set beforehand (e.g., the groundcontact load reference value Fz0_i).

In the case where the ground contact load estimated value Fz_i_estm(i=1, 2, 3, 4) is determined without using the vehicle center of gravitylongitudinal acceleration detected value Accx_sens and the vehiclecenter of gravity lateral acceleration detected value Accy_sens, thereis no need to input Accx_sens and Accy_sens to the vehicle modelcalculator 24.

Subsequently, in S104, the wheel advancing speed vector estimator 24 ecalculates the wheel advancing speed vector ↑Vi_estm of each wheel 2-i.

In this case, the wheel advancing speed vector estimator 24 e calculateseach wheel advancing speed vector estimated value ↑Vi_estm (=(Vx_i_estm,Vy_i_estm)^(T)) according to expression 1-2 given below on the basis ofthe vehicle center of gravity velocity vector estimated value ↑Vg_estm_p(=(Vgx_estm_p, Vgy_estm_p)^(T)) and the yaw rate estimated valueγ_estm_p of the vehicle motional state amount estimated value (theprevious value) calculated by the processing in S114 (the processing bythe vehicle motion estimator 24 d), which will be discussed later, in aprevious arithmetic processing cycle, and each wheel position vector ↑Pi(=(Px_i, Py_i)^(T)) which has been set beforehand.

↑Vi_estm=↑Vg_estm_(—) p+(−Py _(—) i*γ_estm_(—) p, Px _(—) i*γ_estm_(—)p)^(T)   Expression 1-2

Here, the second term of the right side of expression 1-2 means arelative speed of the i-th wheel 2-i with respect to thecenter-of-gravity point of the vehicle 1 (a relative speed in thedirection orthogonal to the yaw-axis direction) produced by a rotationalmotion about the yaw axis of the vehicle 1, i.e., a rotational motion inwhich the value of the yaw rate becomes γ_estm_p.

In place of the yaw rate estimated value (previous value) γ_estm_p ofexpression 1-2, a yaw rate detected value γ_sens (a previous value or acurrent value) may be used.

Subsequently, in S106, the wheel slip rate estimator 24 h calculates thewheel slip rate estimated value κi_estm of each wheel 2-i.

In this case, the wheel slip rate estimator 24 h calculates each wheelslip rate estimated value κi_estm on the basis of the front wheelsteering angle detected value (the current value) δf_sens(=δ1_sens=δ2_sens) of the detected values of the amounts to be observedthat have been obtained in S100, the wheel speed estimated value (theprevious value) Vw_i_estm_p (i=1, 2, 3, 4) calculated by the processingin S116 (the arithmetic processing by the wheel motion estimator 24 f),which will be discussed later, in the previous arithmetic processingcycle, and the wheel advancing speed vector estimated value (the currentvalue) ↑Vi_estm (i=1, 2, 3, 4) calculated in S114.

To be more specific, the wheel slip rate estimator 24 h first calculatesthe wheel advancing speed vector estimated value on the wheel coordinatesystem ↑Vsub_i_estm by coordinate-converting the wheel advancing speedvector estimated value ↑Vi_estm according to expression 1-3 given belowfor each wheel 2-i.

↑Vsub_(—) i_estm=Rot(−δi _(—) sens)*↑Vi_estm   Expression 1-3

In this case, in expression 1-3, the front wheel steering angle detectedvalue δf_sens is used as the values of δ1_sens and δ2_sens for the frontwheels 2-1 and 2-2. Further, in the present embodiment, the rear wheels2-3 and 2-4 are non-steering wheels, so that the values of δ3_sens andδ4_sens in expression 1-3 are zero. Hence, the arithmetic processing ofexpression 1-3 may be omitted for the rear wheels 2-3 and 2-4, because↑Vsub_3_estm=↑V3_estm and ↑Vsub_4_estm=↑V4_estm hold.

If the estimated value of a component in the y-axis directionVsuby_i_estm of the wheel advancing speed vector estimated value on eachwheel coordinate system ↑Vsub_i_estm is not used for the arithmeticprocessing (e.g., the processing in S108), which will be discussedlater, then the estimated value of only the component in the x-axisdirection Vsubx_i_estm of the wheel advancing speed vector estimatedvalue on each wheel coordinate system ↑Vsub_i_estm may be calculated.

Then, the wheel slip rate estimator 24 h calculates the wheel slip rateestimated value κi_estm according to expression 1-4 given below for eachwheel 2-i on the basis of estimated value of only the component in thex-axis direction Vsubx_i_estm of the wheel advancing speed vectorestimated value on each wheel coordinate system ↑Vsub_i_estm calculatedas described above and the wheel speed estimated value (the previousvalue) Vw_i_estm_p.

κi_estm=(Vsubx _(—) i_estm−Vw _(—) i_estm_(—) p)/max(Vsubx _(—) i_estm,Vw _(—) i_estm_(—) p)   Expression 1-4

In this case, when the vehicle 1 is accelerated by imparting the drivingforce from the drive system of the vehicle 1 to the front wheels 2-1 and2-2, which are the driving wheels, Vsubx_i_estm≦Vw_i_estm_p holds, sothat κi_estm≦0 holds. When the vehicle 1 is decelerated by imparting abraking force from the braking system of the vehicle 1 to each wheel2-i, Vsubx_i_estm≧Vw_i_estm_p holds, so that κi_estm≦0 holds.

In place of the wheel speed estimated value (a previous value)Vw_i_estm_p, the wheel speed detected value Vw_i_sens (a previous valueor a current value) may be used. In this case, the wheel motionestimator 24 f, which will be described in detail later, is unnecessary.

Subsequently, in S108, the wheel side slip angle estimator 24 gcalculates the wheel side slip angle estimated value βi_estm of eachwheel 2-i.

In this case, the wheel side slip angle estimator 24 g calculates eachwheel side slip angle estimated value βi_estm on the basis of the frontwheel steering angle detected value βf_sens (=δ1_sens=δ2_sens) of thedetected values of the amounts to be observed, which have been obtainedin S100, and the wheel advancing speed vector estimated value ↑Vi_estm(i=1, 2, 3, 4) calculated in S104.

To be specific, the wheel side slip angle estimator 24 g firstcalculates the wheel position side slip angle estimated value β0 i_estmfor each wheel 2-i according to expression 1-5 given below on the basisof the estimated value of a component in the X-axis direction Vx_i_estmof the wheel advancing speed vector estimated value ↑Vi_estm and theestimated value of a component in the Y-axis direction Vy_i_estm.

β0i_estm=tan⁻¹(Vy _(—) i_estm/Vx _(—) i_estm)   Expression 1-5

Then, wheel side slip angle estimator 24 g calculates the wheel sideslip angle estimated value (βi_estm for each wheel 2-i according toexpression 1-6 given below on the basis of the wheel position side slipangle estimated value β0 i_estm calculated as described above and thesteering angle detected value δi_sens.

βi_estm=β0i_estm−δi _(—) sens   Expression 1-6

In this case, in expression 1-6, the front wheel steering angle detectedvalue δf_sens is used as the values of δ1_sens and δ2_sens for the frontwheels 2-1 and 2-2. Further, in the present embodiment, the rear wheels2-3 and 2-4 are non-steering wheels, so that the values of δ3_sens andδ4_sens in expression 1-6 are zero. Hence, β3_estm=β03_estm holds andβ4_estm=β04_estm holds.

The wheel side slip angle estimated value βi_estm may be calculatedaccording to expression 1-7 given below on the basis of the estimatedvalue of a component in the x-axis direction Vsubx_i_estm and theestimated value of a component in the y-axis direction Vsuby_i_estm ofthe wheel advancing speed vector estimated value on the wheel coordinatesystem ↑Vsub_i_estm calculated according to the aforesaid expression1-3.

βi_estm=tan⁻¹(Vsuby _(—) i_estm/Vsubx i_estm)   Expression 1-7

Subsequently, in S110, the wheel frictional force estimator 24 bcalculates the estimated value of the wheel two-dimensional road surfacereaction force on the wheel coordinate system ↑Fsub_i (=(Fsubx_i_estm,Fsuby_i_estm)^(T)) of each wheel 2-i.

Here, the wheel frictional force estimator 24 b has a frictioncharacteristic model which expresses the relationship between the slipbetween each wheel 2-i and a road surface and the road surface reactionforce acting on the wheel 2-i from the road surface. The frictioncharacteristic model in the present embodiment represents thedriving/braking force Fsubx_i and Fsuby_i of the wheel two-dimensionalroad surface reaction force on the wheel coordinate system ↑Fsub_i asthe frictional force acting on each wheel 2-i from a road surface andthe lateral force Fsuby_i as the functions using the wheel slip rate κiand the wheel side slip angle βi, which indicate the slip state of thei-th wheel 2-i, the ground contact load Fz_i, and the road surfacefrictional coefficient μ as input parameters, as indicated byexpressions 1-8 and 1-9 given below.

Fsubx _(—) i=func_(—) fx _(—) i (κi, βi, Fz _(—) i, μ)   Expression 1-8

Fsuby _(—) i=func_(—) fy _(—) i (κi, βi, Fz _(—) i, μ)   Expression 1-9

In this case, the function func_fx_i (κi, βi, Fz_i, μ) of the right sideof expression 1-8, i.e., a function func_fx_i which defines therelationship between Fsubx_i and κi, βi, Fz_i, μ is represented byexpression 1-8a given below in an example of the present embodiment.

func_(—) fx _(—) i (κi, βi, Fz _(—) i, μ)=μ*Cslp _(—) i (κi)*Cattx _(—)i (βi)*Fz _(—) i   Expression 1-8a

Cslp_i(κi) in this expression 1-8a denotes a coefficient that definesthe characteristic of changes in the driving/braking force Fsubx_icaused by a change in the wheel slip rate κi, and Cattx_i(βi) denotes acoefficient that defines the characteristic of changes in thedriving/braking force Fsubx_i caused by changes in the wheel side slipangle βi (i.e., changes in the lateral force Fsuby_i).

The relationship between Cslp_i(κi) and κi is set as illustrated by, forexample, the graph of FIG. 6( a). In other words, the relationship isset such that the coefficient Cslp_i(κi) becomes a monotonicallydecreasing function relative to the wheel slip rate κi.

More specifically, the relationship between Cslp_i(κi) and κi is setsuch that the value of the function func_fx_i (=driving/braking forceFsubx_i) increases in a negative direction (the direction in which thebraking force increases) as the magnitude of the wheel slip rate κiincreases in a situation wherein κi>0 holds (a situation wherein thevehicle 1 is decelerating), while the value of the function func_fx_i(=driving/braking force Fsubx_i) increases in a positive direction (thedirection in which the driving force increases) as the magnitude of thewheel slip rate κi increases in a situation wherein κi<0 holds (asituation wherein the vehicle 1 is accelerating).

According to the relationship illustrated in FIG. 6( a), the coefficientCslp_i(κi) has a saturation characteristic relative to the wheel sliprate κi. This means that the magnitude of the rate of changes inCslp_i(κi) in response to changes in κi, i.e., the value obtained bydifferentiating Cslp_i(κi) by κi, decreases as the absolute value of κiincreases.

Further, the relationship between the coefficient Cattx_i(βi) and thewheel side slip angle βi is set as illustrated by, for example, thegraph of FIG. 6( b). More specifically, the relationship is set suchthat the value of the coefficient Cattx_i(βi) changes toward 0 from 1 asthe absolute value of the wheel side slip angle βi increases from zero.

In other words, the relationship between Cattx_i(βi) and βi is set suchthat the magnitude of the value of the function func_fx_i(=driving/braking force Fsubx_i) decreases as the absolute value of thewheel side slip angle βi increases. This is because, in general, themagnitude of the lateral force Fsuby_i increases and consequently themagnitude of the driving/braking force Fsubx_i decreases as the absolutevalue of the wheel side slip angle βi increases.

Accordingly, the friction characteristic model represented byexpressions 1-8 and 1-8a indicates that the driving/braking forceFsubx_i of the i-th wheel 2-i is proportional to the road surfacefrictional coefficient μ and the ground contact load Fz_i, the Fsubx_iis a monotonically decreasing function relative to the wheel slip rateκi, and also displays the relationship in which the magnitude of Fsubx_idecreases as the absolute value of the wheel side slip angle βiincreases.

Supplementally, the friction characteristic model represented byexpressions 1-8 and 1-8a as described above corresponds to a first modelof the friction characteristic models in the present invention.

Further, the function func_fy_i (κi, βi, Fz_i, μ) of the right side ofexpression 1-9, i.e., the function func_fy_i defining the relationshipbetween Fsuby_i and κi, βi, Fz_i, μ is represented by expression 1-9agiven below in an example of the present embodiment.

func_(—) fy _(—) i (κi , βi, Fz _(—) i, μ)=μ*Cbeta _(—) i(βi)*Catty _(—)i(κi)*Fz _(—) i   Expression 1-9a

Cbeta_i(βi) in this expression 1-9a denotes a coefficient which definesthe characteristic of changes in the lateral force Fsuby=i caused bychanges in the wheel side slip angle βi, and Catty_i(βi) denotes acoefficient that defines the characteristic of changes in the lateralforce Fsuby_i caused by changes in the wheel slip rate κi (i.e., changesin the driving/braking force Fsubx_i).

The relationship between Cbeta_i(βi) and βi is set, for example, asillustrated by the graph of FIG. 7( a). More specifically, therelationship is set such that the coefficient Cbeta_i(βi) becomes amonotonically decreasing function relative to the wheel side slip angleβi.

To be more specific, the relationship between Cbeta_i(βi) and βi is setsuch that the value of the function func_fy_i (=lateral force Fsuby_i)increases in the negative direction (the right direction of the i-thwheel 2-i) as the magnitude of the wheel side slip angle βi increases ina situation wherein βi>0 holds (a situation wherein Vsuby_i holds),while the value of the function func_fy_i (=lateral force Fsuby_i)increases in the positive direction (the left direction of the i-thwheel 2-i) in a situation wherein βi<0 holds (a situation whereinVsuby_i<0 holds).

According to the relationship illustrated in FIG. 7( a), the coefficientCbeta_i(βi) has a saturation characteristic relative to the wheel sideslip angle βi. This means that the magnitude of the rate of changes inCbeta_i(βi) in response to changes in βi (the value obtained bydifferentiating Cbeta_i(βi) by βi) decreases as the absolute value of βiincreases.

Further, the relationship between the coefficient Catty_i(κi) and thewheel side slip rate κi is set as illustrated by, for example, the graphof FIG. 7( b). More specifically, the relationship is set such that thevalue of the coefficient Catty_i(κi) changes toward 0 from 1 as theabsolute value of the wheel side slip angle κi increases from zero.

In other words, the relationship between Catty_i(κi) and κi is set suchthat the magnitude of the lateral force Fsuby_i as the value of thefunction func_fy_i decreases as the absolute value of the wheel sliprate κi increases. This is because, in general, the magnitude of t thedriving/braking force Fsubx_i increases and consequently the magnitudeof the lateral force Fsuby_i decreases as the absolute value of thewheel slip rate κi increases.

Accordingly, the friction characteristic model represented byexpressions 1-9 and 1-9a exhibits that the lateral force Fsuby_i of thei-th wheel 2-i is proportional to the road surface frictionalcoefficient μ and the ground contact load Fz_i, and the Fsuby_i is amonotonically decreasing function relative to the wheel side slip angleβi, and also displays the relationship in which the magnitude of Fsuby_idecreases as the absolute value of the wheel slip rate κi increases.

Supplementally, the friction characteristic model represented byexpressions 1-9 and 1-9a as described above corresponds to a secondmodel of the friction characteristic models in the present invention.

In S110, the wheel frictional force estimator 24 b determines the wheeltwo-dimensional road surface reaction force estimated value on the wheelcoordinate system ↑Fsub_i of each wheel 2-i by using the frictioncharacteristic model set as described above.

To be more specific, for each wheel 2-i, the wheel frictional forceestimator 24 b computes the right side of expression 1-8a and the rightside of expression 1-9a by using the wheel slip rate estimated valueκi_estm calculated in S106, the wheel side slip angle estimated valueβi_estm calculated in S108, the ground contact load estimated valueFz_i_estm calculated in S102, and the road surface frictionalcoefficient estimated value μ_estm_p calculated by the processing inS122 (the arithmetic processing by the μ estimator 26), which will bediscussed later, in the previous arithmetic processing cycle as thevalues of the input parameters of the function func_fx_i (κi, βi, Fz_i,μ) and func_fy_i (κi, βi, Fz_i, μ), respectively.

Then, the wheel frictional force estimator 24 b sets the value of thefunction func_fx_i determined by the computation of expression 1-8a asthe driving/braking force estimated value Fsubx_i_estm, which is theestimated value of the component in the x-axis direction of theestimated value of the wheel two-dimensional road surface reaction forceon the wheel coordinate system ↑Fsub_i.

The wheel frictional force estimator 24 b also sets the value of thefunction func_fy_i determined by the computation of expression 1-9a asthe lateral force estimated value Fsuby_i_estm, which is the estimatedvalue of the component in the y-axis direction of the estimated value ofthe wheel two-dimensional road surface reaction force on the wheelcoordinate system ↑Fsub_i.

In this case, the value of the coefficient Cslp_i(κi) required tocompute the right side of expression 1-8a is determined from the wheelslip rate estimated value κi_estm according to a map indicating therelationship illustrated in FIG. 6( a). The value of the coefficientCatty_i(βi) required to compute the right side of expression 1-8a isdetermined from the wheel side slip angle estimated value βi_estmaccording to a map indicating the relationship illustrated in FIG. 6(b). The value of Cbeta_i(βi) required to compute the right side ofexpression 1-9a is determined from the wheel side slip rate estimatedvalue βi_estm according to a map indicating the relationship illustratedin FIG. 7( a). The value of Cattx_i(κi) required to compute the rightside of expression 1-9a is determined from the wheel slip rate estimatedvalue κi_estm according to a map indicating the relationship illustratedin FIG. 7( b).

Thus, the driving/braking force estimated value Fsubx_i_estm and thelateral force estimated value Fsuby_i_estm as the estimated values ofthe road surface reaction force (frictional force) dependant upon theroad surface frictional coefficient μ out of the road surface reactionforce acting on each wheel 2-i are calculated by using a latest value ofthe road surface frictional coefficient estimated value μ_estm (theprevious value μ_estm_p) and the friction characteristic model.

Supplementally, in the present embodiment, the function func_fx_i hasbeen set such that the driving/braking force Fsubx_i of each wheel 2-iis proportional to the road surface frictional coefficient μ.Alternatively, however, the function func_fx_i may be set according to,for example, expression 1-8b given below.

func_(—) fx _(—) i(κi, βi, Fz _(—) i, μ)=Cslp2_(—) i(μ, κi)*Cattx _(—)i(βi)*Fz _(—) i   Expression 1-8b

In expression 1-8b, Cslp2_i(μ, κi) denotes a coefficient which definesthe characteristic of changes in the driving/braking force Fsubx_icaused by changes in the road surface frictional coefficient μ and thewheel slip rate κ1, and which is obtained by further generalizingμ*Cslp_i(κi) in expression 1-8a described above.

In this case, the relationship between the coefficient Cslp2_i(μ, κi)and the road surface frictional coefficient μ and the wheel slip rate κiis set as indicated by the graph of FIG. 8 by, for example, a map. Therelationship is set such that the coefficient Cslp2_i(μ, κi) becomes amonotonically decreasing function relative to the wheel slip rate Ki andthe absolute value thereof becomes a monotonically increasing functionrelative to the road surface frictional coefficient μ.

FIG. 8 representatively provides a graph of Cslp2_i(μ, κi) correspondingto the values of three different road surface frictional coefficients μ.

Further, according to the relationship illustrated in FIG. 8, thecoefficient Cslp2_i(μ, κi) has a saturation characteristic relative tothe wheel slip rate κi. This means that the magnitude of the rate ofchanges (the value obtained by partially differentiating Cslp_i(μ, κi)by κi) in the coefficient Cslp_i(μ, κi) in response to an increase in κidecreases as the absolute value of κi increases.

In the case where the function func_fx_i is set as described above, anon-linear relationship can be set between the driving/braking forceFsubx_i of each wheel 2-i and the road surface frictional coefficient μ.

For the function func_fy_i related to the lateral force Fsuby_i of eachwheel 2-i, a coefficient Cbeta2_i (μ, βi) that defines thecharacteristic of changes in the lateral force Fsuby_i caused by changesin the road surface frictional coefficient μ and the wheel side slipangle βi may be used in place of μ*Cbeta_i(βi) in expression 1-9a, aswith the case of the function func_fx_i related to the driving forceFsubx_i.

The function func_fy_i related to the lateral force Fsuby_i of eachwheel 2-i may be configured to take the driving/braking force Fsubx_i asan input parameter in place of the wheel slip rate κi. In this case, asthe value of Fsubx_i, the driving/braking force estimated valueFsubx_i_estm determined as described above using the function func_fx_iof the aforesaid expression 1-8a or 1-8b may be used.

Alternatively, for example, the driving/braking force detected valueFsubx_i_sens determined as follows may be used as the value of Fsubx_i.More specifically, in the aforesaid S100, the driving/braking forcedetected value Fsubx_i_sens is determined according to expression 1-8cgiven below on the basis of the wheel torque detected value Tq_i_sensand the wheel speed detected value Vw_i_sens of each wheel 2-i generatedby the amount-to-be-observed detector 22.

Fsubx _(—) i _(—) sens=Tq _(—) i _(—) sens/Rw _(—) i−Vwdot _(—) i _(—)sens*Iw _(—) i/Rw _(—) i ²   Expression 1-8c

Vwdot_i_sens of the right side of expression 1-8c denotes the temporalchange rate (a differential value) of the wheel speed detected valueVw_i_sens. Predetermined values that have been set in advance are usedas the values of the effective wheel radius Rw_i and the wheel inertialmoment Iw_i in expression 1-8c.

The second term of the right side of expression 1-8c may be replaced bya term ωwdot_i_sens*Iw_i/Rw_i using ωwdot_i_sens, which is adifferential value of the wheel rotational angular velocity detectedvalue ωw_i_sens indicated by an output value of the wheel rotationalangular velocity sensor 8-i.

Referring back to FIG. 4, subsequently in S112, the resultant forcecalculator 24 c calculates the total road surface reaction forceresultant translational force vector estimated value ↑Fg_total_estm andthe total road surface reaction force resultant yaw moment estimatedvalue Mgz_total_estm.

In this case, the resultant force calculator 24 c calculates the totalroad surface reaction force resultant translational force vectorestimated value ↑Fg_total_estm and the total road surface reaction forceresultant yaw moment estimated value Mgz_total_estm on the basis of theground contact load estimated value Fz_i_estm of each wheel 2-icalculated in S102, the driving/braking force estimated valueFsubx_i_estm and the lateral force estimated value Fsuby_i_estm of eachwheel 2-i calculated in S110, and the front wheel steering angledetected value δf_sens (=δ1_sens=δ2_sens) of the detected values of theamounts to be observed that have been obtained in S100.

To be more specific, the resultant force calculator 24 c firstcoordinate-converts the estimated value of the two-dimensional roadsurface reaction force vector on the wheel coordinate system↑Fsub_i_estm (=(Fsubx_i_estm, Fsuby_i_estm)^(T)) onto the wheelcoordinate system for each wheel 2-i according to expression 1-10 givenbelow to calculate the two-dimensional road surface reaction forcevector estimated value ↑Fi_estm=(Fx_i_estm, Fy_i_estm)^(T).

↑Fi _(—) estm=Rot(δi _(—) sens)=↑Fsub _(—) i_estm   Expression 1-10

In this case, regarding the front wheels 2-1 and 2-2 in expression 1-10,the front wheel steering angle detected value δf_sens is used as thevalues for δ1_sens and δ2_sens. Further, in the present embodiment,since the rear wheels 2-3 and 2-4 are non-steering wheels, the values ofδ3_sens and δ4_sens in expression 1-10 are zero. Hence, the arithmeticprocessing of expression 1-10 may be omitted for the rear wheels 2-3 and2-4, because ↑F3_estm=↑Fsub_3_estm and ↑F4_estm=↑Fsub_4_estm hold.

Subsequently, the resultant force calculator 24 c calculates the totalroad surface reaction force resultant translational force vectorestimated value ↑Fg_total_estm (=(Fgx_total_estm, Fgy_total_estm,Fgz_total_estm)^(T)) according to expression 1-11 given below, and alsocalculates the total road surface reaction force resultant yaw momentestimated value Mgz_total_estm according to expression 1-12 given below.

↑Fg_total_estm=(ΣFx _(—) i_estm, ΣFy _(—) i_estm, ΣFz _(—) i_estm)^(T)  Expression 1-11

Mgz_total_estm=Σ(↑Pi×↑Fi_estm)   Expression 1-12

The symbol Σ in expressions 1-11 and 1-12 means the total sum on allwheels 2-i (i=1, 2, 3, 4). “↑Pi×↑Fi_estm” in the right side ofexpression 1-12 denotes the exterior product of the wheel positionvector ↑Pi of the i-th wheel 2-i and the two-dimensional road surfacereaction force vector estimated value ↑Fi_estm, meaning the moment aboutthe yaw axis generated at the center-of-gravity point of the vehicle 1by the two-dimensional road surface reaction force vector estimatedvalue ↑Fi_estm of the i-th wheel 2-i.

Supplementally, the calculation of the component in the yaw axisFgz_total_estm of ↑Fg_total_estm may be omitted.

Subsequently, in S114, the vehicle motion estimator 24 e calculatesprimarily the vehicle center of gravity longitudinal velocity estimatedvalue Vgx_estm as the vehicle motional state amount estimated value, thevehicle center of gravity side slip velocity estimated value Vgy_estm,the yaw rate estimated value γ_estm, the vehicle center of gravitylongitudinal acceleration estimated value Accx_estm, and the vehiclecenter of gravity lateral acceleration estimated value Accy_estm.

Here, the vehicle motion estimator 24 e has a vehicle motion modeldisplaying the relationship between the resultant force of road surfacereaction forces as an external force acting on the vehicle 1 and motionsof the vehicle 1. The vehicle motion model in the present embodiment isrepresented by expressions 1-13 to 1-15 given below.

Fgx_total=m*(Vgdot_(—) x−Vgy*γ)   Expression 1-13

Fgy_total=m*(Vgdot_(—) y−Vgx*γ)   Expression 1-14

Mgz_total=Iz*γdot   Expression 1-15

Expressions 1-13 and 1-14 respectively denote the equations of thedynamics related to the translational motion of the center-of-gravitypoint of the vehicle 1 in the X-axis direction and the Y-axis directionof the vehicle body coordinate system. Similarly, expression 1-15denotes the equation of the dynamics related to the rotational motionabout the yaw axis of the vehicle 1.

The vehicle motion model in the present embodiment is based on theassumption that the road surface on which the vehicle 1 is traveling isa horizontal surface (both the road surface bank angle θbank and theroad surface slope angle θslope are both zero).

In S114, the vehicle motion estimator 24 d calculates the vehiclemotional state amount estimated value by using the vehicle motion modelsrepresented by the above expressions 1-13 to 1-15 and the total roadsurface reaction force resultant translational force vector estimatedvalue ↑Fg_total_estm and the total road surface reaction force resultantyaw moment estimated value Mgz_total_estm calculated in S112. In thiscase, the previous values of some vehicle motional state amountestimated values will be also used for the calculation thereof. Further,some vehicle motional state amount estimated values will be calculatedsuch that they will approach the detected values obtained in S100 (suchthat they will not deviate from the detected values).

To be more specific, the vehicle motion estimator 24 d calculates thevehicle center of gravity longitudinal velocity change rate estimatedvalue Vgdot_x_estm, the vehicle center of gravity side slip velocitychange rate estimated value Vgdot_y_estm, and the yaw angularacceleration estimated value γdot_estm, respectively, according to thefollowing expressions 1-13a to 1-15a derived from the aforesaidexpressions 1-13 to 1-15.

The vehicle motion estimator 24 d further calculates the vehicle centerof gravity longitudinal acceleration estimated value Accx_estm and thevehicle center of gravity lateral acceleration estimated value Accy_estmby the following expressions 1-16a and 1-17a according to thedefinitions of the vehicle center of gravity longitudinal accelerationAccx and the vehicle center of gravity lateral acceleration Accy.

Vgdot_(—) x_estm=Fgx_total_est/m+Vgy_estm_(—) p*γ_estm_(—) p  Expression 1-13a

Vgdot_(—) y_estm=Fgy_total_estm/m−Vgx_estm_(—) p*γ_estm_(—) p  Expression 1-14a

γdot _estm=Mgz_total_estm/Iz   Expression 1-15a

Accx_estm=Vgdot_(—) x_estm−Vgy_estm_(—) p*γ_estm_(—) p   Expression1-16a

Accy_estm=Vgdot_(—) y_estm+Vgx_estm_(—) p*γ_estm_(—) p   Expression1-17a

In this case, Fx_total_estm, Fy_total_estm, and Mgz_total_estm inexpressions 1-13a to 1-15a respectively denote the values calculated inS112 (current values), and Vgy_estm_p, Vgx_estm_p, and γ_estm_prespectively denote the values determined in S114 (previous values) in aprevious arithmetic processing cycle. Further, Vgdot_x_estm inexpression 1-16a and Vgdot_y_estm are the values (current values)calculated by expressions 1-13a and 1-14a, respectively. Further, thevalue of the vehicle mass m in expressions 1-13a and 1-14a and the valueof the vehicle yaw inertial moment Iz in expression 1-15a usepredetermined values that have been set beforehand.

Supplementally, the yaw rate detected value γ_sens (a previous value ora current value) may be used in place of the yaw rate estimated value (aprevious value) γ_estm_p of expression 1-13a and expression 1-14a. Thevehicle center of gravity longitudinal acceleration estimated valueAccx_estm and the vehicle center of gravity lateral accelerationestimated value Accy_estm may be determined by computing the first termof the right side of expression 1-13a and the first term of the rightside of expression 1-14a, respectively. In other words, Accx_estm andAccy_estm may be calculated by expressions 1-16b and 1-17b given below.

Accx_estm=Fgx_total_estm/m   Expression 1-16b

Accy_estm=Fgy_total_estm/m   Expression 1-17b

Subsequently, the vehicle motion estimator 24 d calculates the vehiclecenter of gravity longitudinal velocity provisional estimated valueVgx_predict as the preliminary value of the vehicle center of gravitylongitudinal velocity estimated value, the vehicle center of gravityside slip velocity provisional estimated value Vgy_predict as thepreliminary value of the vehicle center of gravity side slip velocityestimated value, and the yaw rate provisional estimated value γ_predictas the preliminary value of the yaw rate estimated value, respectively,according to expressions 1-18, 1-19, and 1-20 given below on the basisof the vehicle center of gravity longitudinal velocity change rateestimated value Vgdot_x_estm, the vehicle center of gravity side slipvelocity change rate estimated value Vgdot_y_estm, the yaw angularacceleration estimated value γdot_estm, the previous value of thevehicle center of gravity longitudinal velocity estimated valueVgx_estm_p, the previous value of the vehicle center of gravity sideslip velocity estimated value Vgy_estm_p, and the previous value of theyaw rate estimated value γ_estm_p, which have been determined asdescribed above.

Vgx_predict=Vgx_estm_(—) p+Vgdot_(—) x_estm*ΔT   Expression 1-18

Vgy_predict=Vgy_estm_(—) p+Vgdot_(—) y_estm*ΔT   Expression 1-19

γ_predict=γ_estm_(—) p+γdot_estm*ΔT   Expression 1-20

The symbol ΔT in expressions 1-18 to 1-20 denotes the arithmeticprocessing cycle of the controller 20. The right sides of theseexpressions 1-18 to 1-20 correspond to the integral calculation ofVgdot_x_estm, the integral calculation of Vgdot_y_estm, and the integralcalculation of γdot_estm.

Here, in the present embodiment, regarding the yaw rate γ of themotional state amount to be estimated, the vehicle motion estimator 24 ddetermines the yaw rate estimated value γ_estm such that the yaw rateestimated value γ_estm is brought close to the yaw rate detected valueγ_sens (such that the yaw rate estimated value γ does not deviate fromγ_sens). Further, regarding the vehicle center of gravity longitudinalvelocity Vgx, which means the vehicle speed of the vehicle 1, thevehicle motion estimator 24 d determines the vehicle center of gravitylongitudinal velocity estimated value Vgx_estm such that the vehiclecenter of gravity longitudinal velocity estimated value Vgx_estm isbrought close to the vehicle center of gravity longitudinal velocityrecognized from the wheel speed detected value Vw_i_sens (i=1, 2, 3, 4),that is, so as not to cause the vehicle center of gravity longitudinalvelocity estimated value Vgx_estm to deviate from the recognized vehiclecenter of gravity longitudinal velocity.

Then, regarding the yaw rate y, the vehicle motion estimator 24 dcalculates the yaw rate error γestm_err, which is the difference betweenthe yaw rate detected value γ_sens obtained in S100 and the provisionalyaw rate estimated value γ_predict calculated by expression 1-20 asdescribed above, according to expression 1-21 given below.

Further, regarding the vehicle center of gravity longitudinal velocityVgx, the vehicle motion estimator 24 d calculates the vehicle speederror Vgx_estm_err, which is the difference between a selected wheelspeed detected value Vw_i_sens select, which is any one of the wheelspeed detected values Vw_i_sens (i=1, 2, 3, 4) obtained in S100, and avehicle longitudinal speed provisional estimated value Vgx_predictcalculated by expression 1-18 as described above, according toexpression 1-22 given below.

The aforesaid selected wheel speed detected value Vw_i_sens_select is avalue selected from the wheel speed detected value Vw_i_sens (i=1, 2, 3,4) as the one corresponding to an actual vehicle speed detected value(the detected value of the actual vehicle center of gravity longitudinalvelocity Vgx_act) based on the wheel speed detected value Vw_i_sens(i=1, 2, 3, 4).

In this case, when the vehicle 1 is accelerated, a slowest wheel speeddetected value among the wheel speed detected values Vw_i_sens (i=1, 2,3, 4) is selected as the selected wheel speed detected valueVw_i_sens_select. When the vehicle 1 is decelerated, a fastest wheelspeed detected value among the wheel speed detected values Vw_i_sens(i=1, 2, 3, 4) is selected as the selected wheel speed detected valueVw_i_sens_select.

γestm_err=γ_sens−γ_predict   Expression 1-21

Vgx_estm_err=Vw _(—) i_sens_select−Vgx_predict   Expression 1-22

Subsequently, the vehicle motion estimator 24 d determines the finalvalues of the vehicle center of gravity longitudinal velocity estimatedvalue Vgx_estm, the vehicle center of gravity side slip velocityestimated value Vgy_estm, and the yaw rate estimated value γ_estm,respectively, in the current arithmetic processing cycle according toexpressions 1-23 to 1-25 given below.

Vgx_estm=Vgx_predict+Kvx*Vgx_estm_err   Expression 1-23

Vgy_estm=Vgy_predict   Expression 1-24

γ_(—estm=γ)_predict+Kγ*γestm_err   Expression 1-25

Kvx in expression 1-23 and Kγ in expression 1-25 respectively denotegain coefficients having predetermined values (<1) that are setbeforehand. In the present embodiment, as indicated by these expressions1-23 to 1-25, the vehicle center of gravity longitudinal velocityestimated value Vgx_estm is determined by correcting the vehicle centerof gravity longitudinal velocity provisional estimated valueVgx_predict, which has been calculated by the aforesaid expression 1-18(an estimated value on a vehicle motion model), according to a feedbackcontrol law (the proportional law in this case) on the basis of thevehicle speed error Vgx_estm_err calculated by the aforesaid expression1-22 so as to bring the vehicle speed error Vgx_estm_err close to zero.

Further, the vehicle center of gravity side slip velocity provisionalestimated value Vgy_predict calculated by the aforesaid expression 1-19(an estimated value on a vehicle motion model) is directly used as thevehicle center of gravity side slip velocity estimated value Vgy_estm.

The yaw rate provisional estimated value γ_predict calculated by theaforesaid expression 1-20 (an estimated value on a vehicle motion model)is corrected according to the feedback control law (the proportional lawin this case) on the basis of the yaw rate error γ_estm_err, which hasbeen calculated by,the aforesaid expression 1-21, so as to bring the yawrate error γ_estm_err close to zero.

Thus, according to the present embodiment, the vehicle center of gravitylongitudinal velocity estimated value Vgx_estm as the vehicle speed ofthe vehicle 1 on the vehicle motion model is determined such that theestimated value Vgx_estm does not deviate from the selected wheel speeddetected value Vw_i_sens_select as the detected value of the actualvehicle speed, i.e., such that Vgx_estm agrees or substantially agreeswith Vw_i_sens_select. Similarly, the yaw rate estimated value γ_estm asthe yaw rate of the vehicle 1 on the vehicle motion model is determinedsuch that the estimated value γ_estm does not deviate from the yaw ratedetected value γ_sens as the detected value of the actual yaw rateγ_act, i.e., such that γ_estm agrees or substantially agrees withγ_sens.

The above has explained the processing in S114 (the processing by thevehicle motion estimator 24 d) in detail.

The vehicle motion estimator 24 d in the present embodiment hasdetermined the vehicle center of gravity longitudinal velocity estimatedvalue Vgx_estm and the yaw rate estimated value γ_estm such that thesevalues do not deviate from the selected wheel speed detected valueVw_i_sens_select (the detected value of the actual vehicle speed) andthe yaw rate detected value γ_sens, respectively. Alternatively,however, either one or both of Vgx_estm and γ_estm may be arranged toalways agree with one or both Vw_i_sens_select and γ_sens. In this case,the processing for calculating Vgx_estm or γ_estm is unnecessary.

The vehicle motion estimator 24 d has determined Vgdot_x_estm, Vgx_estm,Vgdot_y_estm, Vgy_estm, γ_estm, Accx_estm, and Accy_estm as theestimated values of the vehicle motional state amounts. Alternatively,however, more estimated values of the vehicle motional state amounts maybe determined in addition thereto, as necessary.

For example, in the case where the estimated values of the vehiclemotional state amounts are used to control the vehicle center of gravityside slip angle βg, the vehicle center of gravity side slip angleestimated value βg_estm may be calculated. In this case, the vehiclecenter of gravity side slip angle estimated value βg_estm can becalculated according to expression given below 1-26 from the vehiclecenter of gravity longitudinal velocity estimated value Vgx_estm and thevehicle center of gravity side slip velocity estimated value Vgy_estmdetermined as described above.

βg_estm=tan⁻¹(Vgy_estm/Vgx_estm)   Expression 1-26

Further, in the present embodiment, Accx_estm and Accy_estm among theestimated values of the vehicle motional state amounts determined by thevehicle motion estimator 24 d are used by the slope angle estimator 30and the bank angle estimator 28, which will be respectively described indetail hereinafter, and are not used in the processing by the vehiclemodel calculator 24. Hence, Accx_estm and Accy_estm may be calculated bythe slope angle estimator 30 and the bank angle estimator 28,respectively.

Subsequently, in S116 of FIG. 4, the wheel motion estimator 24 fcalculates the wheel speed estimated value Vw_i_estm of each wheel 2-i.

Here, the wheel motion estimator 24 f has a wheel motion model whichindicates the relationship between the forces acting on each wheel 2-i(the wheel torque Tq_i and the driving/braking force) and the rotationalmotion of each wheel 2-i. The wheel motion model is represented by thefollowing expression 1-27 in the present embodiment.

Tq _(—) i=Fsubx _(—) *Rw _(—) i=Iw _(—) i*(Vwdot_(—) i/Rw _(—) i)  Expression 1-27

“Vwdot_i” in expression 1-27 denotes the temporal change rate (adifferential value) of the wheel speed Vw_i of an i-th wheel 2-i andwill be hereinafter referred to as the wheel speed change rate. The leftside of expression 1-27 means a resultant torque of the wheel torqueTq_i imparted to the i-th wheel 2-i from one or both of the drivingsystem and the braking system of the vehicle 1 and the torque impartedto the wheel 2-i by the driving/braking force Fsubx_i of the i-th wheel2-i.

Then, the wheel motion estimator 24 f first calculates the wheel speedchange rate estimated value Vwdot_i_estm of each wheel 2-i according tothe following expression 1-27a derived from expression 1-27.

Vwdot_(—) i_estm=Rw _(—) i*(Tq _(—) i_sens−Fsubx _(—) i_estm*Rw_(—)i)/Iw _(—) i   Expression 1-27a

In this case, Tq_i_sens of expression 1-27a denotes the detected value(the current value) obtained in S100 on each wheel 2-i, and Fsubx_i_estmdenotes the value (the current value) determined in S110 on each wheel2-i. Predetermined values set beforehand are used as the values of theeffective wheel radius Rw_i and the wheel inertial moment Iw_i of eachwheel 2-i.

Subsequently, the wheel motion estimator 24 f calculates the wheel speedprovisional estimated value Vw_i_predict as the preliminary value of thewheel speed estimated value according to the following expression 1-28for each wheel 2-i on the basis of the wheel speed change rate estimatedvalue Vwdot_i_estm determined as described above and the previous valueof the wheel speed estimated value Vw_i_estm_p.

Vw _(—) i_predict=Vw _(—) i_estm_(—) p+Vwdot_(—) i_estm*ΔT   Expression1-28

Expression 1-28 corresponds to the integral calculation of Vwdot_i_estm.

Here, in the present embodiment, the wheel motion estimator 24 fdetermines the wheel speed estimated value Vw_i_estm such that theestimated value Vw_i_estm approaches the wheel speed detected valueVw_i_sens (such that the estimated value Vw_i_estm does not deviate fromVw_i_sens), as with the calculation of the yaw rate estimated valueγ_estm by the wheel motion estimator 24 d.

Then, according to the following expression 1-29, the wheel motionestimator 24 f calculates, on each wheel 2-i, the wheel speed errorVw_i_estm_err indicating the difference between the wheel speedestimated value Vw_i_sens, which has been obtained in S110, and thewheel speed provisional estimated value Vw_i_predict, which has beencalculated by expression 1-28 as described above.

Vw _(—) i_estm_err=Vw _(—) i_sens−Vw _(—) i_predict   Expression 1-29

Subsequently, the wheel motion estimator 24 f determines, on each wheel2-i, a final wheel speed estimated value Vw_i_estm in the currentarithmetic processing cycle according to the following expression 1-30.

Vw _(—) i_estm=Vw _(—) i_predict+Kvw*Vw _(—) i_estm_err   Expression1-30

“Kvw” in expression 1-30 denotes a gain coefficient of a predeterminedvalue (<1), which has been set beforehand.

Thus, in the present embodiment, each wheel speed estimated valueVw_i_estm is determined by correcting each wheel speed provisionalestimated value Vw_i_predict (an estimated value on a vehicle motionmodel), which has been calculated by the aforesaid expression 1-28,according to a feedback control law (the proportional law in this case)on the basis of the wheel speed error Vw_i_estm_err calculated by theaforesaid expression 1-29 such that Vw_i_estm_err approaches zero.

The description of the processing in S102 to S116 given above is thedetails of the processing carried out by the vehicle model calculator24.

The controller 20 then carries out the processing by the bank angleestimator 28 in S118.

Here, the vehicle motion estimator 24 d calculates the vehicle motionalstate amount estimated value by using the vehicle motion modelconstructed on the assumption that the road surface on which the vehicle1 is traveling is a horizontal surface. Therefore, the vehicle center ofgravity lateral acceleration estimated value Accy_estm means the valueof the acceleration of a motion in the lateral direction (the Y-axisdirection of the vehicle body coordinate system) of thecenter-of-gravity point of the vehicle 1 that has been estimated usingthe vehicle motion model on the assumption that the road surface bankangle θbank is zero.

Meanwhile, as described above, if the actual bank angle θbank act of theroad surface on which the vehicle 1 is actually traveling is not zero,then the actual acceleration sensed by the lateral acceleration sensor15, i.e., an actual sensed-by-sensor lateral accelerationAccy_sensor_act, is obtained by superimposing an acceleration componentin a direction parallel to the lateral direction of the vehicle 1 of thegravitational acceleration (=g*sin((θbank_act)) onto the actual vehiclecenter of gravity lateral acceleration Accy_act(=Vgdot_y_act+Vgx_act*γ). Hence, provided that there is no error of thevehicle center of gravity lateral acceleration detected value Accy_sens,the following expression 2-1 holds.

$\begin{matrix}{{Accy\_ sens} = {{{Accy\_ sensor}{\_ act}}\mspace{115mu} = {{Accy\_ act} + {g*{\sin \left( {\theta \; {bank\_ act}} \right)}}}}} & {{Expression}\mspace{14mu} 2\text{-}1}\end{matrix}$

It is considered, therefore, that the difference between the vehiclecenter of gravity lateral acceleration detected value Accy_sens based onan output of the lateral acceleration sensor 15 (=the detected value ofthe sensed-by-sensor lateral acceleration Accy_sensor) and the vehiclecenter of gravity lateral acceleration estimated value Accy_estm basedon the vehicle motion model (=Accy_Sens−Accy_estm; hereinafter referredto as the vehicle center of gravity lateral acceleration errorAccy_estm_err) depends on the actual bank angle θbank_act and agreeswith the acceleration component in a direction parallel to the lateraldirection of the vehicle body 1B of the gravitational acceleration(=g*sin(θbank_act)) in a steady state.

Accordingly, in the present embodiment, the bank angle estimator 28carries out the processing illustrated by the flowchart of FIG. 9 todetermine the road surface bank angle estimated value θbank_estm.

The bank angle estimator 28 calculates in S118-1 the vehicle center ofgravity lateral acceleration error Accy_estm_err according to thefollowing expression 2-2. More specifically, the vehicle center ofgravity lateral acceleration estimated value Accy_estm calculated by thevehicle motion estimator 24 e in S114 is subtracted from the vehiclecenter of gravity lateral acceleration detected value Accy_sensgenerated by the lateral acceleration detector 22 f in S100 of FIG. 4 tocalculate Accy_estm_err.

Accy_estm_err=Accy_sens−Accy_estm   Expression 2-2

Subsequently, the bank angle estimator 28 calculates in S118-2 the roadsurface bank angle provisional estimated value θbank_pre as thepreliminary value of the road surface bank angle estimated value. Inthis case, the bank angle estimator 28 calculates θbank_pre according tothe following expression 2-3 from the vehicle center of gravity lateralacceleration error Accy_estm_err determined in S118-1.

θbank_pre=sin⁻¹(Accy_estm_err/g)   Expression 2-3

Subsequently, the bank angle estimator 28 determines in S118-3 the roadsurface bank angle estimated value θbank_estm by passing the roadsurface bank angle provisional estimated value θbank_pre, which has beencalculated as described above, through a filter having a low-passcharacteristic (high-cut characteristic).

The above has described the processing in S118 (the processing by thebank angle estimator 28) in detail.

Then, the controller 20 carries out the processing by the slope angleestimator 30 in S120.

Here, as with Accy_estm, the vehicle center of gravity longitudinalacceleration estimated value Accx_estm means the value of theacceleration of a motion in the longitudinal direction (in the X-axisdirection of the vehicle body coordinate system) of thecenter-of-gravity point of the vehicle 1, which has been estimated byusing the vehicle motion model on the assumption that the road surfaceslope angle θslope is zero.

Meanwhile, as with the case of the road surface bank angle θbank, if theactual slope angle θslope_act of the road surface on which the vehicle 1is actually traveling is not zero, then the actual acceleration sensedby the longitudinal acceleration sensor 14, i.e., an actualsensed-by-sensor longitudinal acceleration Accx_sensor_act, is obtainedby superimposing an acceleration component in a direction parallel tothe longitudinal direction of the vehicle body 1B of the gravitationalacceleration (=−g*sin((θslope_act)) onto the actual vehicle center ofgravity longitudinal acceleration Accx_act (=Vgdot_x_act+Vgy_act*γ).Hence, provided that there is no error of the vehicle center of gravitylongitudinal acceleration detected value Accx_sens, the followingexpression 3-1 holds.

$\begin{matrix}\begin{matrix}{{Accx\_ sens} = {{Accx\_ sensor}{\_ act}}} \\{= {{Accx\_ act} - {g*{\sin \left( {\theta \; {slope\_ act}} \right)}}}}\end{matrix} & {{Expression}\mspace{14mu} 3\text{-}1}\end{matrix}$

It is considered, therefore, that the difference between the vehiclecenter of gravity longitudinal acceleration detected value Accx sensbased on an output of the longitudinal acceleration sensor 14 (=thedetected value of the sensed-by-sensor longitudinal accelerationAccx_sensor) and the vehicle center of gravity longitudinal accelerationestimated value Accx estm based on the vehicle motion model(=Accx_sens−Accx_estm; hereinafter referred to as the vehicle center ofgravity longitudinal acceleration error Accx_estm_err) depends on theactual slope angle θslope_act and agrees with the acceleration componentin a direction parallel to the longitudinal direction of the vehiclebody 1B of the gravitational acceleration (=−g*sin(θslope_act)) in asteady state.

Accordingly, the slope angle estimator 30 carries out the processingsimilar to that carried out by the bank angle estimator 28 to calculatethe road surface slope angle estimated value θslope_estm.

To be more specific, the slope angle estimator 30 carries out theprocessing illustrated by the flowchart of FIG. 10 so as to determinethe road surface slope angle estimated value θslope_estm.

The slope angle estimator 30 calculates in S120-1 the vehicle center ofgravity longitudinal acceleration error Accx_estm_err according to thefollowing expression 3-2. More specifically, the vehicle center ofgravity longitudinal acceleration estimated value Accx_estm calculatedby the vehicle motion estimator 24 e in S114 is subtracted from thevehicle center of gravity longitudinal acceleration detected valueAccx_sens generated by the longitudinal acceleration detector 22 e inS100 of FIG. 4 to calculate Accx_estm_err.

Accx_estm_err=Accx_sens−Accx_estm   Expression 3-2

Subsequently, the slope angle estimator 30 calculates in S120-2 the roadsurface slope angle provisional estimated value θslope_pre as thepreliminary value of the road surface slope angle estimated value. Inthis case, the slope angle estimator 30 calculates θslope_pre accordingto the following expression 3-3 from the vehicle center of gravitylongitudinal acceleration error Accx_estm_err determined in S120-1.

θslope_pre=−sin⁻¹(Accx_estm_err/g)   Expression 3-3

Subsequently, the slope angle estimator 30 determines in S120-3 the roadsurface slope angle estimated value θslope_estm by passing the roadsurface slope angle provisional estimated value θslope_pre, which hasbeen calculated as described above, through a filter having a low-passcharacteristic (high-cut characteristic).

The above has described the processing in S120 (the processing by theslope angle estimator 30) in detail.

Subsequently, the controller 20 carries out the processing by the μestimator 26 in S122.

Before describing the processing in detail, the principle for estimatingthe road surface frictional coefficient μ in the present embodiment willbe first described.

In this case, for the convenience of explanation, it is assumed that thedynamics of the actual vehicle 1 is approximately represented by thefollowing expression 4-1.

$\begin{matrix}{{{{\frac{}{t}\begin{bmatrix}{Vgy\_ act} \\{\gamma\_ act}\end{bmatrix}} = {\frac{1}{Vgx\_ act}*\begin{bmatrix}{A\; 11} & \begin{matrix}{{- {Vgx\_ act}^{2}} +} \\{A\; 12s}\end{matrix} \\{A\; 21} & {A\; 22}\end{bmatrix}*\begin{bmatrix}{Vgy\_ act} \\{\gamma\_ act}\end{bmatrix}}}\quad} + {\quad{{\begin{bmatrix}{B\; 1} \\{B\; 2}\end{bmatrix}*\delta \; {f\_ act}} - {\begin{bmatrix}g \\0\end{bmatrix}*{\sin \left( {\theta \; {bank\_ act}} \right)}}}}} & {{Expression}\mspace{14mu} 4\text{-}1}\end{matrix}$

where A11=−2*(CPf+CPr)/m

-   -   A12s=−2*(Lf*CPf−Lr*CPr)/m    -   A21=−2*(Lf*CPf−Lr*CPr)/Iz    -   A22=−2*(Lf²*CPf+Lr²*CPr)/Iz    -   B1=2*CPf/m    -   B2=2*Lf*CPf/Iz    -   CPf: Cornering power of the front wheel of the 2-wheel model    -   CPr: Cornering power of the rear wheel of the 2-wheel model

More detailedly, this expression 4-1 denotes a dynamic model which is aso-called two-wheeled model (a linear two-wheeled model) whichapproximately represents a side slip motion of the actual vehicle 1 anda rotational motion about the yaw axis as dynamic behaviors of a modelvehicle having one front wheel serving as a steering control wheel andone rear wheel serving as a non-steering control wheel.

The cornering power CPf of the front wheel in this two-wheeled modelcorresponds to the cornering power per wheel of the front wheels 2-1 and2-2 of the actual vehicle (a 4-wheel vehicle). The cornering power CProf the rear wheel in the two-wheeled model corresponds to the corneringpower per wheel of the rear wheels 2-3 and 2-4 of the actual vehicle 1(the 4-wheel vehicle).

Here, the cornering power CPf per wheel of the front wheels 2-1 and 2-2on a reference road surface on which the value of the actual roadsurface frictional coefficient μ_act is 1 is denoted by CPf0, and thecornering power CPr per wheel of the rear wheels 2-3 and 2-4 on thereference road surface is denoted by CPr0. At this time, a proportionalrelationship approximately holds between each of the cornering powersCPf and CPr on a road surface having the actual road surface frictionalcoefficient μ_act of an arbitrary value and the actual road surfacefrictional coefficient μ_act, as indicated by expressions 4-2a and 4-2bgiven below.

Cpf=CPf0*μ_act   Expression 4-2a

CPr=Cpr0*μ_act   Expression 4-2b

Applying the expressions 4-2a and 4-2b to expression 4-1 given aboverewrites expression 4-1 to expression 4-3 given below.

$\begin{matrix}{{\frac{}{t}\begin{bmatrix}{Vgy\_ act} \\{\gamma\_ act}\end{bmatrix}} = {{\frac{1}{Vgx\_ act}*\begin{bmatrix}{{\mu\_ act}*a\; 11} & \begin{matrix}{{- {Vgx\_ act}^{2}} +} \\{{\mu\_ act}*a\; 12s}\end{matrix} \\{{\mu\_ act}*a\; 21} & {{\mu\_ act}*a\; 22}\end{bmatrix}*\begin{bmatrix}{Vgy\_ act} \\{\gamma\_ act}\end{bmatrix}} + {\quad{{\begin{bmatrix}{{\mu\_ act}*b\; 1} \\{{\mu\_ act}*b\; 2}\end{bmatrix}*\delta \; {f\_ act}} - {\begin{bmatrix}g \\0\end{bmatrix}*\left( {\theta \; {bank\_ act}} \right)}}}}} & {{Expression}\mspace{14mu} 4\text{-}3}\end{matrix}$

where a11=−2*(CPf0+CPr0)/m

-   -   a12s=−2*(Lf*CPf0−Lr*CPr0)/m    -   a21=−2*(Lf*CPf0−Lr*CPr0)/Iz    -   a22=−2*(Lf²*CPf0+Lr²*CPr0)/Iz    -   b1=2*CPf0/m    -   b2=2*Lf*CPf0/Iz

Based on this expression 4-3, which represents the linear two-wheeledmodel, the following will explain a method for estimating the roadsurface frictional coefficient μ by using a moment about the yaw axis,i.e., the aforesaid NSP yaw moment Mnsp generated at the neutral steerpoint (NSP) of the vehicle 1.

First, the technological meaning of the actual NSP yaw moment Mnsp_actrelated to the estimation of the road surface frictional coefficient μand a method for identifying or estimating the value of the actual NSPyaw moment Mnsp_act from the observed value of the state amount of amotion of the vehicle 1 associated therewith will be described.

The left side of the first line of expression 4-3 means the differentialvalue of the actual vehicle center of gravity side slip velocity Vgy_act(temporal change rate), i.e., the actual vehicle center of gravity sideslip velocity change rate Vgdot_y_act. Therefore, the first line ofexpression 4-3 can be rewritten to the following expression 4-4.

$\begin{matrix}{{{{Vgdot\_ y}{\_ act}} + {{Vgx\_ act}*{\gamma\_ act}} + {g*{\sin \left( {\theta \; {bank\_ act}} \right)}}} = {{{\mu\_ act}*a\; 11*{{Vgy\_ act}/{Vgx\_ act}}} + {{\mu\_ act}*a\; 12s*{{\gamma\_ act}/{Vgx\_ act}}} + {{\mu\_ act}*b\; 1*\delta \; {f\_ act}}}} & {{Expression}\mspace{14mu} 4\text{-}4}\end{matrix}$

Meanwhile, expression 4-5 given below is derived from the definition ofthe vehicle center of gravity lateral acceleration Accy(Accy=Vgdot_y+Vgx*γ) and the aforesaid expression 2-1 related to thesensed-by-sensor lateral acceleration Accy_sensor.

Accy_sensor_act=Vgdot_(—) y_act+Vgx_act*γ_act+g*sin(θbank_act)  Expression 4-5

This expression 4-5 indicates that the left side of expression 4-4agrees with the actual sensed-by-sensor lateral accelerationAccy_sensor_act. Thus, the following expression 4-6 is derived fromexpressions 4-4 and 4-5.

Accy_sensor_act=μ_act*a11*Vgy_act/Vgx_act+μ_(act)*a12s*γ_act/Vgx_act+μ_act*b1*δf_act   Expression 4-6

The right side of this expression 4-6 corresponds to the value obtainedby dividing a component in the lateral direction of the vehicle body 1Bin the translational force vector acting on the center-of-gravity pointof the vehicle 1 due to the resultant force of the actual road surfacereaction forces acting on each wheel 2-i from a road surface (i.e., acomponent in the X-axis direction Fgy_total_act of the actual total roadsurface reaction force resultant translational force vector↑Fg_total_act) by the vehicle mass m. Hence, expression 4-6 represents arelationship in which Accy_sensor_act (=Accy_act+g*sin(θbank_act))agrees with Fgy_total_act/m.

The left side of the expression of the second line of expression 4-3means the differential value (the temporal change rate) of the actualyaw rate γ_act, that is, the actual yaw angular acceleration γdot_act,so that the expression of the second line of expression 4-3 can berewritten to expression 4-7 given below.

γ_dot_act=μ_act*a21*Vgy_act/Vgx_act+μ_act*a22*γ_act/Vgx_act+μ_(act*)b2*δf_act   Expression 4-7

The right side of this expression 4-7 corresponds to the value obtainedby dividing a moment about the yaw axis acting on the center-of-gravitypoint of the vehicle 1 due to the resultant force of the actual roadsurface reaction forces acting on each wheel 2-i from a road surface(i.e., an actual total road surface reaction force resultant yaw momentMgz_act) by a vehicle yaw inertial moment Iz. Hence, expression 4-7represents a relationship in which γdot_act agrees with Mgz_act/Iz.

Taking the above expressions 4-6 and 4-7 as simultaneous equations,eliminating Vy_act results in the following expression 4-8.

$\begin{matrix}{{{\gamma dot\_ act} - {\left( {a\; {21/a}\; 11} \right)*{Accy\_ sensor}{\_ act}}} = {{\mu\_ act}*\begin{pmatrix}{\left( {{a\; 22} - {\left( {a\; {21/a}\; 11} \right)*\; a\; 12s}} \right)*} \\{{{\gamma\_ act}/{Vgx\_ act}} + {\left( {{b\; 2} - {\left( {a\; {21/a}\; 11} \right)*b\; 1}} \right)*\delta \; {f\_ act}}}\end{pmatrix}}} & {{Expression}\mspace{14mu} 4\text{-}8}\end{matrix}$

Here, as described above, NSP means the load application point (theworking point) of the resultant force of the lateral forces Fsuby_i(i=1, 2, 3, 4) acting on all the wheels 2-i (i=1, 2, 3, 4) when thevehicle center of gravity side slip angle βg occurs while the vehicle 1is traveling in the situation wherein δ1=δ2=0 holds. Therefore, in thedynamic model of the vehicle 1 represented by the aforesaid expression4-3, the relationship indicated by expression 4-9 given below holdsbetween the distance Lnsp between the vehicle center of gravity and NSP,which is the distance between the center-of-gravity point of the vehicle1 and NSP, and the cornering powers CPf0 and CPr0 of the aforesaidreference road surface.

Lnsp=−(Lf*CPf0−Lr*CPr0)/(CPf0+CPr0)   Expression 4-9

Further, expression 4-10 given below is derived from the aboveexpression 4-9 and the definitions of a11 and a21 given in the note ofthe aforesaid expression 4-2.

a21/a11=−Lnsp*m/Iz   Expression 4-10

Then, applying the derived expression 4-10 to the left side ofexpression 4-8 given above rewrites expression 4-8 to the followingexpression 4-11.

$\begin{matrix}{{{{{Iz}*{\gamma dot\_ act}} + {{Lnsp}*m*{Accy\_ sensor}{\_ act}}} = {{\mu\_ act}*{p\left( {{\gamma\_ act},{\delta f\_ act},{Vgx\_ act}} \right)}}}\mspace{20mu} {where}} & {{Expression}\mspace{14mu} 4\text{-}11} \\{{p\left( {{\gamma\_ act},{\delta f\_ act},{Vgx\_ act}} \right)} = {{Iz}*\begin{pmatrix}{\left( {{a\; 22} - {\left( {a\; {21/a}\; 11} \right)*a\; 12s}} \right)*} \\{{{\gamma\_ act}/{Vgx\_ act}} + {\left( {{b\; 2} - {\left( {a\; {21/a}\; 11} \right)*b\; 1}} \right)*\delta \; {f\_ act}}}\end{pmatrix}}} & {{Expression}\mspace{14mu} 4\text{-}12}\end{matrix}$

Both sides of expression 4-11 mean an actual moment about the yaw axisat NSP (an actual NSP yaw moment Mnsp_act). More specifically, theactual NSP yaw moment Mnsp_act agrees with the left side and the rightside of expression 4-11, as indicated by expressions 4-13a and 4-13bgiven below.

Mnsp_act=Iz*γdot_act+Lnsp*m*Accy_sensor_act   Expression 4-13a

Mnsp_act=μ_act*p(γ_act, δf_act, Vgx_act)   Expression 4-13b

Expression 4-13a represents the actual NSP yaw moment Mnsp_act as anexternal force moment (a moment with a sign reversed from the sign of anactual inertial force moment) balancing out the actual inertial forcemoment about the yaw axis generated at NSP by a motion of the vehicle 1(a moment component of an actual inertial force).

The first term of the right side of expression 4-13a corresponds to anexternal force moment (i.e., the actual total road surface reactionforce resultant yaw moment Mgz_total_act) balancing out the actualinertial force moment about the yaw axis generated at thecenter-of-gravity point of the vehicle 1 by a motion of the vehicle 1.

The second term of the right side of expression 4-13b corresponds to amoment (=Lnsp*Fgy_total_act) generated about the yaw axis at NSP by atranslational external force (i.e., the component in the Y-axisdirection of the vehicle body coordinate system Fgy_total_act of theactual total road surface reaction force resultant translational forcevector ↑Fg_total_act) balancing out an actual translational inertialforce (a translational force component of an actual inertial force) inthe Y-axis direction of the vehicle body coordinate system generated atthe center-of-gravity point of the vehicle 1 by a motion of the vehicle1.

Expression 4-13b represents the actual NSP yaw moment Mnsp_act as theactual moment about the yaw axis acting on NSP due to the resultantforce of actual road surface reaction forces acting on each wheel 2-ifrom a road surface, depending on the actual road surface frictionalcoefficient μ_act.

As is obvious from the aforesaid expression 4-13b, p(γ_act, δf_act,Vgx_act) defined by expression 4-12 denotes the ratio of an incrementalamount of Mnsp_act relative to an incremental amount of μ_act (adifferential value of Mnsp_act based on μ_act). In other words, p(γ_act,δf_act, Vx_act) means the sensitivity of Mnsp_act to a change in μ_act(hereinafter referred to as the μ sensitivity). Further in other words,p(γ_act, δf_act, Vgx_act) denotes the actual NSP yaw moment Mnsp_act inthe case where μ_act=1 holds (in the case where μ_act is 1), that is,the actual road surface frictional coefficient μ_act agrees with thefrictional coefficient of the reference road surface.

Here, the right sides of both expressions 4-13a and 4-13b do not includethe actual vehicle center of gravity side slip velocity Vgy_act and theactual road surface bank angle θbank_act. It is known therefore that thevalue of the actual NSP yaw moment Mnsp_act is defined without dependingdirectly on the values of the actual vehicle center of gravity side slipvelocity Vgy_act and the actual road surface bank angle θbank_act.

More specifically, when the actual vehicle center of gravity side slipvelocity Vgy_act changes or the actual road surface bank angle θbank_actchanges, the moment component of the first term and the moment componentof the second term of the right side of the aforesaid expression 4-13achange; however, the moment components basically change in oppositedirections from each other.

Thus, the changes in the moment components of the first term and thesecond term, respectively, of expression 4-13a caused by a change inVgy_act or a change in θbank_act take place such that the changes canceleach other. As a result, the actual NSP yaw moment Mnsp_act is hardlyinfluenced by a change in Vgy_act or a change in θbank_act.

Further, as is obvious from expression 4-13b, the actual NSP yaw momentMnsp_act changes depending on the actual road surface frictionalcoefficient μ_act and the μ sensitivity p without depending directly onthe value of Vgy_act or θbank_act in a situation wherein the μsensitivity p(γ_act, δf_act, Vgx_act) is not zero (p≠0).

When attention is focused on expression 4-13a out of the aforesaidexpressions 4-13a and 4-13b, it is understood that observing the actualyaw angular acceleration γdot_act and the actual sensed-by-sensorlateral acceleration Accy_sensor_act makes it possible to identify thevalue of the actual NSP yaw moment Mnsp_act generated by the resultantforce of actual road surface reaction forces acting on each wheel 2-ifrom a road surface on the basis of the observed values of γdot_act andAccy_sensor_act. The actual road surface reaction forces depend upon theactual road surface frictional coefficient μ_act.

In this case, the right side of expression 4-13a does not include notonly the actual road surface frictional coefficient μ_act but also theactual vehicle center of gravity lateral acceleration Vgy_act and theactual road surface bank angle θbank_act. Thus, the observed value ofthe actual NSP yaw moment Mnsp_act can be obtained from the observedvalues of the actual yaw angular acceleration γdot_act and the actualsensed-by-sensor lateral acceleration Accy_sensor_act without the needfor the observed values of the actual road surface frictionalcoefficient μ_act, the actual vehicle center of gravity lateralacceleration Vgy_act, and the actual road surface bank angle θbank_act.

Here, the aforesaid yaw angular acceleration detected value γdot_sensmeans the observed value of the actual yaw angular accelerationγdot_act, while the aforesaid vehicle center of gravity lateralacceleration detected value Accy_sens means the observed value of theactual sensed-by-sensor lateral acceleration Accy_sensor_act.

Hence, the values calculated by an expression in which γdot_act andAccy_sensor_act of the right side of expression 4-13a have been replacedby γdot_sens and Accy_sens, which are the observed values thereof, willbe hereinafter referred to as the NSP yaw moment detected valueMnsp_sens. This Mnsp_sens is defined by expression 4-14 given below.

Mnsp_sens=Iz*γdot_sens+Lnsp*m*Accy_sens   Expression 4-14

In this case, if it is assumed that the yaw angular accelerationdetected value γdot_sens and the vehicle center of gravity lateralacceleration detected value Acct_sens accurately agree with the actualyaw angular acceleration detected value γdot_act and the actualsensed-by-sensor lateral acceleration Accy_sensor_act, then Mnsp_actequals Mnsp_sens. Accordingly, from the yaw angular accelerationdetected value γdot_sens and the vehicle center of gravity lateralacceleration detected value Accy_sens, the NSP yaw moment detected valueMnsp_sens as the observed value of the actual NSP yaw moment Mnsp_actcan be calculated by expression 4-14.

The NSP yaw moment detected value Mnsp_sens calculated as describedabove carries a meaning as the value (detected value) of Mnsp estimatedon the basis of the observed value of a motional state amount of thevehicle 1 without the need for the value of the actual external force(actual road surface reaction force) acting on the vehicle 1 or thevalue of the actual road surface frictional coefficient μ_act.

The description will now be given of the processing in which theestimated value of the road surface frictional coefficient μ is used toestimate the road surface reaction forces acting on a wheel of thevehicle 1 on an appropriate dynamic model of the vehicle 1 in place ofthe aforesaid NSP yaw moment detected value Mnsp_sens and then the valueof the NSP yaw moment generated by the resultant force of the estimatedroad surface reaction forces is estimated.

Here, in the present embodiment, the road surface reaction forceestimated value is calculated by the vehicle model calculator 24 asdescribed above by using a friction characteristic model or a vehiclemotion model. Then, the value of the NSP yaw moment Mnsp can beestimated from the estimated value of the road surface reaction force,as will be discussed later.

However, in the description herein, for the convenience of explainingthe principle of estimating the road surface frictional coefficient μ, avehicle model calculator, which is different from the vehicle modelcalculator 24 (hereinafter referred to as the vehicle model calculatorfor the explanation) will sequentially carries out the arithmeticprocessing for estimating the motional state amount of the vehicle 1 orthe road surface reaction force at a predetermined arithmetic processingcycle by using the dynamic model of the vehicle 1 represented by theaforesaid expression 4-3.

In this case, at each arithmetic processing cycle, the latest values(the previous values or the current values) of the vehicle center ofgravity longitudinal velocity estimated value Vgx_estm, the road surfacefrictional coefficient estimated value μ_estm, and the road surface bankangle estimated value θbank_estm as the observed values of the frontwheel steering angle detected value δf_sens, the yaw rate detected valueγ_sens, and the road surface bank angle estimated value θbank_estm areinput to the vehicle model calculator for the explanation as theobserved values of δf_act, γ_act, Vgx_act, μ_act, and θbank_act,respectively, of the right side of expression 4-3.

Incidentally, Vgx_estm, μ_estm, and θbank_estm mean the observed valuesobtained by an arbitrary appropriate method. The values of parametersa11, a12 s, a21, a22, b1, and b2 in the aforesaid expression 4-3 are tobe preset.

Then, the vehicle model calculator for the explanation carries out thefollowing estimation arithmetic processing. More specifically, thevehicle model calculator for the explanation calculates the vehiclecenter of gravity side slip velocity change rate estimated valueVgdot_y_estm, which is the estimated value of the temporal change rate(differential value) of the vehicle center of gravity side slip velocityVgy, according to the following expression 5-1, in which the actualvalue of γ_act or the like in the expression of the first line of theaforesaid expression 4-3 has been replaced by an estimated value or adetected value.

$\begin{matrix}{{{Vgdot\_ y}{\_ estm}} = {{{\mu\_ estm}*\; a\; 11*{Vgy\_ estm}{{\_ p}/{Vgx\_ estm}}} + {{\mu\_ estm}*a\; 12s*{{\gamma\_ sens}/{Vgx\_ estm}}} + {{\mu\_ estm}*b\; 1*\delta \; {f\_ sens}} - {{Vgx\_ estm}*{\gamma\_ sens}} - {g*{\sin ({\theta bank\_ estm})}}}} & {{Expression}\mspace{14mu} 5\text{-}1}\end{matrix}$

The vehicle center of gravity side slip velocity estimated valueVgy_estm_p required for the computation of the first term of the rightside of expression 5-1 is the previous value as the latest value ofVgy_estm already calculated by the vehicle model calculator for theexplanation.

In this case, the result obtained by removing the fourth term and thefifth term from the right side of expression 5-1 carries a meaning as avalue obtained by dividing the estimated value of a lateral component ofthe vehicle body 1B of the translational force vector acting on thecenter-of-gravity point of the vehicle 1 due to the resultant force ofthe road surface reaction forces of each wheel 2-i (i.e., the estimatedvalue of a component in the Y-axis direction of the total road surfacereaction force resultant translational force vector ↑Fg_total) by thevehicle mass m.

The fourth term of the right side means the estimated value of theacceleration generated at the center-of-gravity point of the vehicle 1due to a centrifugal force from a turning motion of the vehicle 1, andthe fifth term means the estimated value of the lateral accelerationcomponent of the vehicle body 1B of the gravitational acceleration.

Accordingly, expression 5-1 denotes the processing for calculating thevehicle center of gravity side slip velocity change rate estimated valueVgdot_y_estm by calculating Fgy_total_estm/m on the basis of μ_estm,

Vgy_estm_p, Vgx_estm, γ_sens, and δf_sens, and then by subtracting theestimated value of the acceleration of the centrifugal force acting onthe center-of-gravity point of the vehicle 1 (=Vgx_estm*γ_sens) and theestimated value of an acceleration component in the lateral direction ofthe vehicle body 1B out of the gravitational acceleration(=g*sin(θbank_estm)) from the calculated value of Fgy_total_estm/m.

Then, the vehicle model calculator for the explanation calculates a newvehicle center of gravity side slip velocity estimated value Vgy_estm (acurrent value) according to the following expression 5-2 indicating theintegral calculation of Vgdot_y_estm on the basis of the vehicle centerof gravity side slip velocity change rate estimated value Vgdot_y_estmdetermined as described above and the previous value of the vehiclecenter of gravity side slip velocity estimated value Vgy_estm_p. Inexpression 5-2, ΔT denotes the arithmetic processing cycle of thevehicle model calculator for the explanation.

Vgy_estm=Vgy_estm_(—) p+Vgdot_(—) y_estm*ΔT   Expression 5-2

The value of Vgy_estm calculated as described above is used to calculatethe new vehicle center of gravity side slip velocity change rateVgdot_y_estm at the next arithmetic processing cycle.

Further, the vehicle model calculator for the explanation calculates thesensed-by-sensor lateral acceleration estimated value Accy_sensor_estm,which is the estimated value of the actual acceleration sensed by thelateral acceleration sensor 15 of the vehicle 1 (the actualsensed-by-sensor lateral acceleration Accy_sensor_act) according toexpression 5-3 given below (in other words, by the calculation of thefirst to the third terms of the right side of expression 5-1).

Accy_sensor_estm=μ_estm*a11*Vgy_estm_(—)p/Vgx_estm+μ_estm*a12s*γ_sens/Vgx_estm+μ_estm*b1*δf_sens   Expression5-3

Supplementally, regarding this expression 5-3, the following expression5-4 holds, as is obvious from the aforesaid expression 4-5.

Accy_sensor_estm=Vgdot_(—) y_estm+Vgx_estm*γ_sens+g*sin(θbank_estm)  Expression 5-4

Further, as is obvious from this expression 5-4 and the aforesaidexpression 5-1, the right side of expression 5-4 agrees with the sum ofthe first to the third terms of the right side of expression 5-1. Hence,the sensed-by-sensor lateral acceleration estimated valueAccy_sensor_estm can be calculated according to the aforesaid expression5-3.

The right side of expression 5-3 means the value obtained by dividingthe estimated value of a component in the lateral direction of thevehicle body 1B of the translational force vector acting on thecenter-of-gravity point of the vehicle 1 due to the resultant force ofthe road surface reaction force of each wheel 2-i (i.e., the estimatedvalue of a component in the Y-axis direction Fgy_total_estm of the totalroad surface reaction force resultant translational force vector↑Fg_total) by the vehicle mass m. Therefore, expression 5-3 denotes theprocessing for calculating Vgy_total_estm/m on the basis of μ_estm,Vgy_estm_p, Vgx_estm, γ_sens, and δf_sens, and then obtaining thecalculated Fgy_total_estm/m as Accy_sensor_estm.

Further, the vehicle model calculator for the explanation calculates theyaw angular acceleration estimated value γdot_estm, which is theestimated value of the temporal change rate (a differential value) ofthe yaw angular acceleration γdot, according to the following expression5-5 obtained by replacing the actual value of γ_act or the like in theexpression of the second line of the aforesaid expression 4-3.

γdot_estm=μ_estm*a21*Vgy_estm_(—)p/Vgx_estm+μ_estm*a22*γ_sens/Vgx_estm+μ_estm*b2*δf_sens   Expression 5-5

The right side of this expression 5-5 means the arithmetic processingfor determining the value obtained by dividing the estimated value of amoment about the yaw axis acting on the center-of-gravity point of thevehicle 1 due to the resultant force of the road surface reaction forcesof each wheel 2-i (i.e., the total road surface reaction force resultantyaw moment estimated value Mgz_estm) by a vehicle yaw inertial momentIz. Therefore, expression 5-5 denotes the processing for calculatingMgz_estm/Iz on the basis of μ_estm, Vgy_estm_p, Vgx_estm, γ_sens, andδf_sens, and then obtaining the calculated value of Mgz_estm/Iz as theyaw angular acceleration estimated value γdot_estm.

Here, eliminating Vgy_estm, taking the above expressions 5-3 and 5-5 assimultaneous equations, and applying the aforesaid expression leads toexpression 5-6 given below.

$\begin{matrix}{{{{{Iz}*{\gamma dot\_ estm}} + {{Lnsp}*m*{Accy\_ sensor}{\_ estm}}} = {{\mu\_ estm}*{p\left( {{\gamma\_ sens},{\delta f\_ sens},{Vgx\_ estm}} \right)}}}\mspace{20mu} {where}} & {{Expression}\mspace{14mu} 5\text{-}6} \\{{p\left( {{\gamma\_ sens},{\delta f\_ sens},{Vgx\_ estm}} \right)} = {{Iz}*\begin{pmatrix}\begin{matrix}{\left( {{a\; 22} - {\left( {a\; {21/a}\; 11} \right)*a\; 12\; s}} \right)*} \\{{{\gamma\_ sens}/{Vgx\_ estm}} +}\end{matrix} \\{\left( {{b\; 2} - {\left( {a\; {21/a}\; 11} \right)*b\; 1}} \right)*\delta \; {f\_ sens}}\end{pmatrix}}} & {{Expression}\mspace{14mu} 5\text{-}7}\end{matrix}$

Incidentally, p(γ_sens, δf_sens, Vgx_estm) means the value of the μsensitivity calculated from γ_sens, δf_sens, and Vgx_estm, which are theobserved values of γ, δf, and Vgx. In the following description, the μsensitivity p will mean p(γ_sens, δf_sens, Vgx_estm) defined by theabove expression 5-7 unless otherwise specified.

More generally, the μ sensitivity p defined by expression 5-7 denotesthe value of the μ sensitivity calculated by linearly coupling γ_sensand δf_sens. In this case, if the coefficients by which γ_sens andδf_sens are multiplied are denoted by A1 and A2, respectively, (ifp=A1*γ_sens+A2*δf_sens), then A1=Iz*((a22−(a21/a11)*a12 s)/Vgx_estm andA2=(b2−(a21/a11)*b1) hold. Therefore, the coefficients A1 and A2 may besaid to be the coefficients that are set such that A1 and A2 changeaccording to Vgx_estm as the observed value of the vehicle speed of thevehicle 1 (such that A2/A1 changes in proportion to Vgx_estm).

In other words, the linear coupling of γ_sens and δf_sens by expression5-7 may be said to be the linear coupling configured such that the valueof the μ sensitivity p calculated by the linear coupling is proportionalto the value of the actual NSP yaw moment Mnsp_act identified using theobserved values or the detected values γ_sens, δf_sens, and Vgx_estm asthe values of γ_act, δf_act, and Vgx_act in the case where it is assumedthat the road surface frictional coefficient μ_act takes a constantvalue in the linear two-wheeled vehicle model denoted by the aforesaidexpression 4-3.

Supplementally, in the present embodiment, the yaw rate estimated valueγ_estm is determined such that the value γ_estm agrees or substantiallyagrees with the yaw rate detected value γ_sens, as described above.Hence, an expression in which γ_sens in the right side of the aforesaidexpression 5-7 has been replaced by γ_estm may be used as a definitionalexpression for determining the value of the μ sensitivity p.

Both sides of the above expression 5-6 mean an NSP yaw moment estimatedvalue Mnsp_estm, which is the estimated value of a moment about the yawaxis at NSP (the value of a moment on a model based on the aforesaidexpression 4-3). In other words, the NSP yaw moment estimated valueMnsp_estm agrees with the left side and the right side of expression5-6, as indicated by expressions 5-8a and 5-8b given below.

Mnsp_estm=Iz*γdot_estm+Lnsp*m*Accy_sensor_estm   Expression 5-8a

Mnsp_estm=μ_estm*p(γ_sens, δf_sens, Vgx_estm)   Expression 5-8b

Expression 5-8a represents the NSP yaw moment estimated value Mnsp_estmas the estimated value of a moment balancing out an inertial forcemoment (a moment with a sign reversed from the sign of the inertialforce moment) generated about the yaw axis at NSP by a motion of thevehicle 1 on the model.

Expression 5-8b represents the NSP yaw moment estimated value Mnsp_estmas the estimated value of a moment about the yaw axis generated at NSPdue to the resultant force of the road surface reaction forces of eachwheel 2-i, which depends on μ_estm (the resultant force of road surfacereaction forces on the model).

In this case, the NSP yaw moment estimated value Mnsp_estm calculated byexpression 5-8b out of expressions 5-8a and 5-8b is calculated dependingon the road surface frictional coefficient estimated value μ_estm, sothat the Mnsp_estm reflects an influence of an error of the road surfacefrictional coefficient estimated value μ_estm.

The right side of expression 5-8b does not directly include the vehiclecenter of gravity lateral acceleration estimated value Vgy_estm or theroad surface bank angle estimated value θbank_estm. For this reason, theNSP yaw moment estimated value Mnsp_estm calculated by expression 5-8bwill not be directly subjected to the influence of an error of thevehicle center of gravity lateral acceleration estimated value Vgy_estmor the road surface bank angle estimated value θbank_estm.

Accordingly, the vehicle model calculator for the explanation calculatesthe NSP yaw moment estimated value Mnsp_estm by expression 5-8b. Furthergeneralizing the NSP yaw moment estimated value Mnsp_estm thuscalculated, the estimated value Mnsp_estm carries a meaning as theestimated value of Mnsp_act calculated depending on μ_estm on the basisof a dynamic model of the vehicle 1 (more specifically, the estimatedvalue of Mnsp_act calculated on the assumption that μ_estm is accurate).

The above has described the processing by the vehicle model calculatorfor the explanation. Supplementally, for the convenience of explanationof the principle for estimating the road surface frictional coefficientμ, the vehicle model calculator for the explanation has calculated thevehicle center of gravity side slip velocity change rate estimated valueVgdot_y_estm, the vehicle center of gravity side slip velocity estimatedvalue Vgy_estm, the yaw angular acceleration estimated value γdot_estm,and the sensed-by-sensor lateral acceleration estimated valueAccy_sensor_estm.

However, if the NSP yaw moment estimated value Mnsp_estm is calculatedaccording to the aforesaid expression 5-8b on the basis of the dynamicmodel (the linear two-wheeled vehicle model) represented by theaforesaid expression 4-3, then Vgdot_y_estm, Vgy_estm, γdot_estm, andAccy_sensor_estm are not required, as is obvious from the aforesaidexpressions 5-7 and 5-8b.

If the dynamic model represented by the aforesaid expression 4-3 isused, then the value of the calculation result of the right side of theaforesaid expression 5-8a and the value of the calculation result of theright side of the aforesaid expression 5-8b will be the same. Therefore,Mnsp_estm may alternatively be calculated by expression 5-8a.

A method for estimating the road surface frictional coefficient μ willnow be discussed on the basis of the NSP yaw moment detected valueMnsp_sens obtained by the aforesaid expression 4-14 and the NSP yawmoment estimated value Mnsp_estm calculated by the aforesaid expression5-8b.

As described above, Mnsp_sens carries a meaning as the observed value(detected value) of Mnsp_act obtained on the basis of the observed valueof the state amount of a motion of the vehicle 1 (γdot_sens, Accy_sens)without the need for the value of a road surface reaction force actingon the vehicle 1 as an external force or the value of the road surfacefrictional coefficient μ. Similarly, Mnsp_estm carries a meaning as theobserved value (estimated value) of Mnsp_act calculated using μ_estm onthe basis of a dynamic model of the vehicle 1. Hence, the differencebetween Mnsp_sens and Mnsp_estm is considered to have correlation withthe error of μ_estm relative to μ_act.

Here, it is assumed that the yaw rate detected value γ_sens, the yawangular acceleration detected value γ_dot_sens, the front wheel steeringangle detected value δf_sens, the vehicle center of gravity longitudinalvelocity estimated value Vgx_estm (the estimated value of a vehiclespeed), and the vehicle center of gravity lateral acceleration detectedvalue Accy_sens accurately coincide with the actual yaw rate γ_act, theactual yaw angular acceleration γdot_act, the actual front wheelsteering angle detected value δf_act, the actual vehicle center ofgravity longitudinal velocity Vgx_act, and the actual sensed-by-sensorlateral acceleration Accy_sensor_act, respectively. At this time,expression 6-1 given below is derived from the aforesaid expression4-11.

Iz*γdot_sens+Lnsp*m*Accy_sens=μ_act*p(γ_sens, δf_sens, Vgs_estm)  Expression 6-1

Further, expression 6-2 given blow is derived from this expression 6-1and the aforesaid expressions 4-14, 5-6, and 5-8b.

$\begin{matrix}\begin{matrix}{{{Mnsp\_ sens} - {Mnsp\_ estm}} = {\begin{pmatrix}{{{Iz}*{\gamma dot\_ sens}} +} \\{{Lnsp}*m*{Accy\_ sens}}\end{pmatrix} -}} \\{\begin{pmatrix}{{{Iz}*{\gamma dot\_ estm}} +} \\\begin{matrix}{{Lnsp}*m*} \\{{Accy\_ sensor}{\_ estm}}\end{matrix}\end{pmatrix}} \\{= {\left( {{{\mu\_ act} - {\mu\_ estm}}} \right)*}} \\{{p\left( {{\gamma\_ sens},{\delta f\_ sens},{Vgx\_ estm}} \right)}}\end{matrix} & {{Expression}\mspace{14mu} 6\text{-}2}\end{matrix}$

Based on this expression 6-2, the road surface frictional coefficientestimated value μ_estm may be determined such that Mnsp_estm coincideswith Mnsp_sens in order to cause the value of μ_estm to coincide withthe actual road surface frictional coefficient μ_act in a situationwherein p(γ_sens, δf_sens, and Vgx_estm) is not zero (≠0).

More generally, this means that the road surface frictional coefficientestimated value μ_estm to be applied to the dynamic model may bedetermined such that the estimated value of the actual NSP yaw momentMnsp_act (the NSP yaw moment estimated value Mnsp_estm) calculated usinga dynamic model including the friction characteristic of each wheel 2-iof the vehicle 1 (a dynamic model dependant upon the road surfacefrictional coefficient estimated value μ_estm) agrees with the estimatedvalue of the actual NSP yaw moment Mnsp act (NSP yaw moment detectedvalue Mnsp_sens) calculated from the yaw angular acceleration detectedvalue γdot_sens as the observed value of a motional state amount of thevehicle 1 and the vehicle center of gravity lateral accelerationdetected value Accy_sens (=the detected value of the sensed-by-sensorlateral acceleration Accy_sensor).

In this case, p(γ_sens, δf_sens, Vgx_estm) of the right side ofexpression 6-2 does not include the vehicle center of gravity side slipvelocity estimated value Vgy_estm or the road surface bank angleestimated value θbank_estm, as is obvious from the aforesaid expression5-7. Therefore, in the situation wherein p(γ_sens, δf_sens, Vgx_estm) isnot zero (≠0), the value of the difference between Mnsp_sens andMnsp_estm (the left side of expression 6-2) is considered to have highcorrelation with the difference between μ_act and μ_estm, i.e., theerror of μ_estm. In other words, in the situation wherein p(γ_sens,δf_sens, Vgx_estm) is not zero (≠0), the difference between Mnsp_sensand Mnsp_estm is considered primarily due to the error of μ_estm.

Accordingly, it is considered that determining the road surfacefrictional coefficient estimated value μ_estm on the basis of expression6-2 makes it possible to estimate the actual road surface frictionalcoefficient μ_act while restraining the influence of the error of thevehicle center of gravity side slip velocity estimated value Vgy_estm orthe road surface bank angle estimated value θbank_estm. Thus, the μestimator 26 in the present embodiment calculates the road surfacefrictional coefficient estimated value μ_estm on the basis of theaforesaid expression 6-2.

To determine the road surface frictional coefficient estimated valueμ_estm on the basis of expression 6-2 as described above such thatMnsp_estm coincides with Mnsp_sens in the situation wherein p(γ_sens,δf_sens, Vgx_estm) is not zero (≠0), it is conceivable to determine theroad surface frictional coefficient estimated value μ_estm such that,for example, the following expression 6-3 is satisfied.

Mnsp_sens=μ_estm*p(γ_sens, δf_sens, Vgx_estm)   Expression 6-3

In this case, however, the road surface frictional coefficient estimatedvalue μ_estm tends to develop an undue change due to errors ofMnsp_sens, γ_sens, δf_sens, and Vx_sens. Especially when the value ofp(γ_sens, δf_sens, Vgx_estm) is close to zero, it is difficult to securethe reliability and stability of the road surface frictional coefficientestimated value μ_estm determined on the basis of expression 6-3.

Hence, the μ estimator 26 in the present embodiment carries out feedbackarithmetic processing based on the difference between the NSP yaw momentdetected value Mnsp_sens determined from the observed value of amotional state amount of the vehicle 1 and the NSP yaw moment estimatedvalue Mnsp_estm determined on the basis of a road surface reactionforce, which is estimated depending on the road surface frictionalcoefficient estimated value μ_estm, so as to sequentially determine theincreasing/decreasing manipulated variable of μ_estm such that thedifference converges to zero, i.e., such that Mnsp estm converges toMnsp_sens.

The μ estimator 26 updates the value of μ_estm on the basis of thedetermined increasing/decreasing manipulated variable. Thus, the valueof μ_estm is sequentially calculated such that the road surfacefrictional coefficient estimated value μ_estm converges to the actualroad surface frictional coefficient μ_act (steadily agrees with μ_act).Hereinafter, the difference between Mnsp_sens and Mnsp_estm(=Mnsp_sens-Mnsp_estm) will be referred to as the NSP yaw momentestimation error Mnsp_err.

In this case, as is obvious from the aforesaid expression 6-2, the NSPyaw moment estimation error Mnsp_err is proportional to the μsensitivity p. As the μ sensitivity p approaches zero, the sensitivityof Mnsp_err to the error to μ_estm (the magnitude of the ratio of achange in Mnsp_err with respect to a change in the error of μ_estm)decreases.

In the present embodiment, therefore, the gain value, which indicatesthe ratio of a change in the increasing/decreasing manipulated variableof μ_estm with respect to a change in Mnsp_err (i.e., the feedback gainof the feedback arithmetic processing for converging Mnsp_err to zero),is changed according to the μ sensitivity p in order to secure thereliability and stability of μ_estm.

The above has described the basic principle for estimating the roadsurface frictional coefficient μ in the present embodiment.

Based on the basic principle for estimating the road surface frictionalcoefficient μ explained above, the processing by the μ estimator 26 inthe present embodiment will be described with reference to FIG. 11 toFIG. 13.

As illustrated in the block diagram of FIG. 11, the μ estimator 26includes, as its functions, an Mnsp_sens calculator 26 a, whichcalculates the NSP yaw moment detected value Mnsp_sens, an Mnsp_estmcalculator 26 b, which calculates an NSP yaw moment estimated valueMnsp_estm, an Mnsp_err calculator 26 c, which calculates the NSP yawmoment estimation error Mnsp_err, a μ sensitivity calculator 26 d, whichcalculates the μ sensitivity p(γ_sens, δf_sens, Vgx_estm), a frictionalcoefficient increasing/decreasing manipulated variable determiner 26 e,which determines the increasing/decreasing manipulated variable Δμ ofthe road surface frictional coefficient μ, and a frictional coefficientestimated value updater 26 f, which updates the road surface frictionalcoefficient estimated value μ_estm on the basis of theincreasing/decreasing manipulated variable Δμ.

The μ estimator 26 carries out the processing illustrated by theflowchart of FIG. 12 thereby to sequentially determine the road surfacefrictional coefficient estimated value μ_estm.

More specifically, the μ estimator 26 carries out the processing by anMnsp_sens calculator 26 a in S122-1 to calculate the NSP yaw momentdetected value Mnsp_sens.

To be more specific, the Mnsp_sens calculator 26 a computes the rightside of the aforesaid expression 4-14 by using the yaw angularacceleration detected value γdot_sens as the observed value of amotional state amount of the vehicle 1 associated with an inertial forcemoment balancing out the NSP yaw moment Mnsp and the vehicle center ofgravity lateral acceleration detected value Accy_sens (thesensed-by-sensor lateral acceleration detected value) out of theamount-to-be-observed detected values generated by theamount-to-be-observed detector 22 in the aforesaid S100.

In this case, predetermined values set in advance are used as the valueof the vehicle yaw inertial moment Iz, the value of the vehicle mass m,and the distance Lnsp between the vehicle center of gravity and the NSP,which are necessary to compute expression 4-14.

The first term of the right side of expression 4-14 corresponds to atotal road surface reaction force resultant force yaw moment detectedvalue Mgz_total_sens, and “m*Accy_sens” in the second term correspondsto the total road surface reaction force resultant lateral forcedetected value Fgy_total_sens.

Further, the μ estimator 26 carries out the processing by an Mnsp estmcalculator 26 b in S122-2 to calculate the NSP yaw moment estimatedvalue Mnsp_estm.

To be more specific, the Mnsp_estm calculator 26 b calculates Mnsp_estmaccording to the following expression 7-1 on the basis of the total roadsurface reaction force resultant lateral force estimated valueFgy_total_estm (a component in the Y-axis direction of the total roadsurface reaction force resultant translational force vector estimatedvalue ↑Fg_total_estm) and the total road surface reaction forceresultant yaw moment estimated value Mgz_total_estm, which have beencalculated by the vehicle model calculator 24 in the aforesaid S112.

Mnsp_estm=Mgz_total_estm+Lnsp*Fgy_total_estm   Expression 7-1

Subsequently, the μ estimator 26 carries out the processing by theMnsp_err calculator 26 c in S122-3 to calculate the NSP yaw momentestimation error Mnsp_err. To be more specific, the Mnsp_err calculator26 c calculates Mnsp_err by subtracting the NSP yaw moment estimatedvalue Mnsp_estm calculated in S122-2 from the NSP yaw moment detectedvalue Mnsp_sens calculated in S122-1.

Further, the μ estimator 26 calculates the μ sensitivity p by carryingout the processing by the μ sensitivity calculator 26 d in S122-4.

To be more specific, the μ sensitivity calculator 26 d calculates the μsensitivity p(γ_sens, δf_sens, Vgx_estm) by carrying out the calculationof the right side of the aforesaid expression 5-7 from the yaw ratedetected value y sens and the front wheel steering angle detected valueδf_sens, which have been generated by the amount-to-be-observed detector22 in the aforesaid S100, and the vehicle center of gravity longitudinalvelocity estimated value Vgx_estm determined by the vehicle modelcalculator 24 in the aforesaid S114. In this case, predetermined valuesthat are set beforehand are used as the value of the vehicle inertialyaw moment Iz and the values of the parameters a11, a12 s, a21, a22, b1and b2, which are necessary for the calculation of expression 5-7.

In this case, as is obvious from expression 5-7, the μ sensitivity p isdetermined by linearly coupling γ_sens and δf_sens. In this linearcoupling, the ratio between a coefficient by which γ_sens is multipliedand a coefficient by which δf_sens is multiplied changes according toVgx_estm.

Subsequently, the μ estimator 26 carries out the processing by thefrictional coefficient increasing/decreasing manipulated variabledeterminer 26 e in S122-5 to determine a frictional coefficientincreasing/decreasing manipulated variable Δμ.

To schematically explain the processing, basically, the frictionalcoefficient increasing/decreasing manipulated variable determiner 26 edetermines the frictional coefficient increasing/decreasing manipulatedvariable Δμ on the basis of the NSP yaw moment estimation error Mnsp_errcalculated in S122-3 (more specifically, on the basis of Mnsp_err andthe μ sensitivity p calculated in S122-4).

To be more specific, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e determines the frictionalcoefficient increasing/decreasing manipulated variable Δμ according tothe feedback control law such that the NSP yaw moment error Mnsp_err isconverged to zero, i.e., such that Mnsp estm is converged to Mnsp_sens.In this case, the proportional law is used as the feedback control law,and the Δμ is calculated by multiplying Mnsp_err by a given gain valueGmu. Further, in this case, Δμ is determined to be proportional to theproduct of Mnsp_err and the aforesaid μ sensitivity p. Thus, the gainvalue Gmu indicative of the ratio of a change in Δμ with respect to achange in Mnsp_err (hereinafter, Gmu will be referred to as thefrictional coefficient operating gain) is determined such that the gainvalue Gmu changes according to the μ sensitivity p.

Here, Mnsp_sens and Mnsp_estm carry a meaning as different approaches ormethods for estimating the value of the same actual NSP yaw momentMnsp_act.

The polarity (direction) of the actual NSP yaw moment Mnsp_act can beeither the positive polarity or the negative polarity, depending on thetraveling condition of the vehicle 1. Hence, in a situation whereinMnsp_act is not zero (Mnsp_act≠0), Mnsp_sens and Mnsp_estm should denotemoments that share the same polarity, i.e., the moments in the samedirection.

In a situation wherein Mnsp_sens and Mnsp_estm have polarities that areopposite to each other, it is considered that the error of Mnsp_estm isrelatively large, as compared with the absolute value of Mnsp_sens orMnsp_estm, and the reliability of the value of Mnsp_sens or Mnsp_estm islow, i.e., the S/N ratio is low.

Accordingly, there is a danger in such a situation that updating theroad surface frictional coefficient estimated value μ_estm on the basisof the NSP yaw moment estimation error Mnsp_err calculated fromMnsp_sens and Mnsp_estm leads to a further increase in the absolutevalue of Mnsp_err with the consequent divergence of the road surfacefrictional coefficient estimated value μ_estm.

According to the present embodiment, therefore, in the case where apredetermined updating cancellation condition, which includes at least acondition that the polarities of Mnsp_sens and Mnsp_estm are different,that is, opposite from each other, the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e cancelsdetermining the frictional coefficient increasing/decreasing manipulatedvariable Δμ on the basis of Mnsp_err (i.e., the updating of the roadsurface frictional coefficient estimated value μ_estm on the basis ofMnsp_err), and determines a predetermined value that has been setbeforehand as the value of Δμ.

To be more specific, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e carries out the processing asillustrated by the flowchart of FIG. 13.

The frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e first determines in S122-5-1 whether a condition thatMnsp_estm>Mm and Mnsp_sens>Ms or a condition that Mnsp_estm<−Mm andMnsp_sens<−Ms holds on the NSP yaw moment detected value Mnsp_senscalculated in S122-1 and the NSP yaw moment estimated value Mnsp_estmcalculated in S122-2. The reference characters Mm and Ms denotenon-negative predetermined values (zero or positive values in thevicinity of zero), which are set beforehand.

The determination processing in S122-5-1 determines whether theaforesaid updating cancellation condition holds. If the determinationresult of S122-5-1 is negative, then it means that the updatingcancellation condition holds.

In this case, if the predetermined values Mm and Ms are set to zero,then the determination result of S122-5-1 will be negative, that is, theupdating cancellation condition will hold. This is equivalent toMnsp_estm and Mnsp_sens having polarities that are opposite from eachother.

Meanwhile, if the predetermined values Mm and Ms are positive values,then the determination result in S122-5-1 will be negative, meaning thatthe updating cancellation condition applies, not only in the case whereMnsp_estm and Mnsp_sens have polarities that are opposite from eachother but also in the case where −Mm≦Mnsp_estm≦Mm or −Ms≦Mnsp_sens≦Msholds (in other words, in the case where Mnsp_estm or Mnsp_sens takes avalue in a range in the vicinity of zero).

In this case, therefore, the updating cancellation condition includes acondition that at least one of Mnsp_estm and Mnsp_sens takes a valuewithin the predetermined range in the vicinity of zero in addition tothe condition that the polarities of Mnsp_estm and Mnsp_sens areopposite to each other.

Subsequently, in S122-5-2 or S122-5-3, the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e sets a gainadjustment parameter Kmu_att for adjusting the aforesaid frictionalcoefficient operation gain Gmu (a parameter by which the NSP yaw momenterror Mnsp_err is multiplied, together with the μ sensitivity p)according to the determination result in S122-5-1.

To be more specific, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e sets the value of Kmu_att to 1 inS122-5-2 if the determination result in S122-5-1 is affirmative, thatis, the updating cancellation condition does not hold. If thedetermination result is negative, that is, if the updating cancellationcondition applies, then the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e sets the value of Kmu_att to zeroin S122-5-3.

The processing of S122-5-1 to S122-5-3 described above is the processingcarried by the gain adjustor in FIG. 11. The dashed-line arrow in FIG.11 indicates that the value of the μ sensitivity p is input to the gainadjustor, which is related to a third embodiment or a fourth embodimentto be discussed later. In the present embodiment, the processing by thegain adjustor does not use the value of the μ sensitivity p.

Subsequently, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e calculates in S122-5-4 thefrictional coefficient increasing/decreasing manipulated variable Δμaccording to the following expression 7-2.

$\begin{matrix}\begin{matrix}{{\Delta \; \mu} = {{Mnsp\_ err}*{Gmu}}} \\{= {{Mnsp\_ err}*\begin{pmatrix}{{p\begin{pmatrix}{{\gamma\_ sens},{\delta f\_ sens},} \\{Vgx\_ estm}\end{pmatrix}}*} \\{{Kmu}*{Kmu\_ att}}\end{pmatrix}}}\end{matrix} & {{Expression}\mspace{14mu} 7\text{-}2}\end{matrix}$

More specifically, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e determines, as the frictionalcoefficient operation gain Gmu, a value obtained by multiplying the μsensitivity p calculated in S122-4 by a basic gain Kmu, which is apreset positive predetermined value, and a gain adjustment parameterKmu_att set on the basis of the determination result in S122-5-1(=p*Kmu*Kmu_att). Then, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e multiplies the NSP yaw moment errorMnsp_err calculated in S122-3 by the obtained frictional coefficientoperation gain Gmu so as to determine the frictional coefficientincreasing/decreasing manipulated variable Δμ.

In this case, the frictional coefficient operation gain Gmu in the casewhere the determination result in S122-5-1 is negative (where theupdating cancellation condition does not apply) has the same polarity asthat of the μ sensitivity p and Gmu is determined such that themagnitude (the absolute value) of Gmu decreases as the magnitude (theabsolute value) of the μ sensitivity p decreases.

Further, if the determination result of S122-5-1 is affirmative (if theupdating cancellation condition applies), then the value of the gainadjustment parameter Kmu_att is set to zero, causing the frictionalcoefficient operation gain Gmu to be set to zero. This forcibly sets thefrictional coefficient increasing/decreasing manipulated variable Δμ tozero.

The above has described the processing carried out by the frictionalcoefficient increasing/decreasing manipulated variable determiner 26 ein S122-5.

Referring back to FIG. 12, the μ estimator 26 then carries out theprocessing by the frictional coefficient estimated value updater 26 f inS122-6 to update the road surface frictional coefficient estimated valueμ_estm.

To be more specific, the frictional coefficient estimated value updater26 f adds the frictional coefficient increasing/decreasing manipulatedvariable Δμ calculated in S122-5 to the previous value of the roadsurface frictional coefficient estimated value μ_estm_p so as to updatethe road surface frictional coefficient estimated value μ_estm from theprevious value μ_estm_p, thereby determining a new road surfacefrictional coefficient estimated value μ_estm (the current value ofμ_estm).

In other words, this processing is carried out to determine the roadsurface frictional coefficient estimated value μ_estm by integrating Δμ.In this case, if the determination result in S122-5-1 is affirmative (ifthe updating cancellation condition applies), then Δμ becomes zero(Δμ=0), so that the current value of the road surface frictionalcoefficient estimated value μ_estm is retained at the previous valueμ_estm_p.

In other words, in a situation wherein the determination result inS122-5-1 is affirmative, the road surface frictional coefficientestimated value μ_estm is retained at the road surface frictionalcoefficient estimated value μ_estm determined lastly in the situationwherein the determination result in S122-5-1 is negative.

The above has described the details of the processing by the μ estimator26 in the present embodiment.

Supplementally, in the present embodiment, the processing by the vehiclemodel calculator 24 (the processing of S102 to S116 in FIG. 4) and theprocessing for the NSP yaw moment estimated value Mnsp_estm by the μestimator 26 (S122-2 in FIG. 12) together implement the function of afirst estimator of a to-be-compared external force in the presentinvention.

In this case, Mnsp_estm corresponds to a first estimated value of ato-be-compared external force in the present invention. Further, thedetected values of the amounts to be observed (ε1_sens, δ2_sens,Vw_i_sens, γ_sens, Accx_sens, Accy_sens, Tq_i_sens) input to the vehiclemodel calculator 24 correspond to the observed values of thepredetermined types of amounts to be observed in the present invention.The detected values of the amounts to be observed (δ1_sens, δ2_sens,Vw_i_sens, γ_sens, Accx_sens, Accy_sens, Tq_i_sens) are the detectedvalues of the amounts to be observed that are necessary for identifyingthe values of input parameters (κi, βi, Fz_i) other than the roadsurface frictional coefficient μ among the input parameters in theaforesaid friction characteristic model.

The steps from S102 to S116 in the processing carried by the vehiclemodel calculator 24 implements the function of the vehicle motion/roadsurface reaction force estimator in the present invention.

In this case, the vehicle motion side slip velocity Vgy_estm correspondsto the state amount of a side slip motion of a vehicle in the presentinvention. Further, the relationship represented by the aforesaidexpression 1-14 corresponds to the dynamic relationship associated withthe vehicle motion/road surface reaction force estimator. The processingin S122-2 of FIG. 12 may alternatively be carried out by the vehiclemodel calculator 24.

In the present embodiment, the processing for determining the NSP yawmoment detected value Mnsp_sens by the μ estimator 26 (S122-1 of FIG.12) implements the function of a second estimator of a to-be-comparedexternal force in the present invention.

In this case, Mnsp_sens corresponds to a second estimated value of ato-be-compared external force in the present invention. The yaw angularacceleration detected value γdot_sens and the vehicle center of gravitylateral acceleration detected value Accy_sens (the sensed-by-sensorlateral acceleration detected value Accy_sensor_sens) correspond to theobserved values of motional state amounts of the vehicle 1 that definethe inertial moment about the yaw axis at NSP (the inertial forcecorresponding to a to-be-compared external force).

Further, the processing by the μ sensitivity calculator 26 d of the μestimator 26 (the processing in S122-4 of FIG. 12) corresponds to theprocessing by the μ sensitivity calculating means in the presentinvention, the processing by the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e (theprocessing in S122-5 of FIG. 12) corresponds to the processing by thefrictional coefficient increasing/decreasing manipulated variabledetermining means in the present invention, and the processing by thefrictional coefficient estimated value updater 26 f (the processing inS122-6 of FIG. 12) corresponds to the processing by the frictionalcoefficient estimated value updating means in the present invention.

Further, the determination processing in S122-5-1 of the processingcarried out by the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e corresponds to the processing bythe updating cancellation condition determining means in the presentinvention.

The same correspondence relationship between the present embodimentdescribed above and the present invention will be applied to a secondembodiment to an eighth embodiment, which will be discussed hereinafter,except for the updating cancellation condition determiner.

In the present embodiment explained above, the frictional coefficientincreasing/decreasing manipulated variable Δμ is determined such thatthe NSP yaw moment error Mnsp_err, which indicates the differencebetween the NSP yaw moment detected value Mnsp_sens and the NSP yawmoment estimated value Mnsp_estm, is converged to zero in the case wherethe updating cancellation condition does not apply.

This arrangement makes it possible to determine the value of μ_estmwhile restraining the error of the estimated value of the state amountof a side slip motion of the vehicle 1, such as the vehicle center ofgravity side slip velocity estimated value Vgy_estm, or restraining achange in the actual road surface bank angle θ_act from influencing theroad surface frictional coefficient estimated value μ_estm. Thus, highlyreliable μ_estm can be stably determined.

In the case where the updating cancellation condition does not apply,the road surface frictional coefficient estimated value μ_estm isdetermined such that estm is proportional to the product of the NSP yawmoment error Mnsp_err and the μ sensitivity p calculated by linearlycoupling γ_sens and δf_sens indicated by the aforesaid expression 5-7.Consequently, the frictional coefficient operation gain Gmu is set suchthat the magnitude of Gmu decreases as the magnitude of the μsensitivity p decreases.

This arrangement makes it possible to prevent the road surfacefrictional coefficient estimated value μ_estm from being excessivelyupdated in a situation wherein the value of the μ sensitivity p is zeroor close to zero, i.e., in a situation wherein the Mnsp_err is likely toinclude relatively many unwanted components that do not depend on anerror of the road surface frictional coefficient estimated value μ_estm.

Thus, the robustness of the estimation of the road surface frictionalcoefficient μ can be enhanced, and the Mns_err can be reflected inupdating the road surface frictional coefficient estimated value μ_estmaccording to the degree of dependence of Mnsp_err on the error of theroad surface frictional coefficient estimated value μ_estm. As a result,the estimation accuracy of the road surface frictional coefficient μ canbe enhanced and the robustness of the estimation processing can beenhanced.

Further, in a situation wherein the NSP yaw moment detected valueMnsp_sens and the NSP yaw moment estimated value Mnsp_estm carrypolarities that are opposite from each other, the determination resultin S122-5-1 becomes. negative (the updating cancellation conditionapplies), so that the value of the gain adjustment parameter Kmu_att isset to zero. Consequently, the Δμ is forcibly set to zero.

Accordingly, the updating of the road surface frictional coefficientestimated value μ_estm based on Mnsp_err is cancelled and μ_estm ismaintained at a value immediately before the determination result inS122-5-1 turns to be negative.

This arrangement makes it possible to prevent the road surfacefrictional coefficient estimated value μ_estm from diverging in thesituation wherein Mnsp_sens and Mnsp_estm have opposite polarities.

Supplementally, in the case where the predetermined values Mm and Ms inthe determination processing in S122-5-1 are set to positive values, ifthe Mnsp sens or Mnsp_estm takes a value in a range in the vicinity ofzero, as described above, then the determination result in S122-5-1 willbe negative, so that the value of Δμ will be forcibly set to zero.

Thus, it is possible to cancel the updating of μ_estm based on Mnsp_errin the case where Mnsp_estm and Mnsp_sens have opposite polarities andalso in the case where the error of Mnsp_sens or Mnsp_estm is likely tobe relatively large, as compared with the magnitude of the actual NSPyaw moment Mnsp_act.

In the present embodiment, the value of the gain adjustment parameterKmu_att has been determined on the basis of the determination result inS122-5-1. Alternatively, however, the value of Δμ may be determinedaccording to the aforesaid expression 7-2 without using Kmu_att in thecase where the determination result in S122-5-1 is affirmative, or thevalue of Δμ may be set to zero in the case where the determinationresult is negative.

Second Embodiment

A second embodiment of the present invention will now be described withreference to FIG. 14 and FIG. 15. The present embodiment differs fromthe aforesaid first embodiment only in the method for setting the gainadjustment parameter Kmu_att in a frictional coefficientincreasing/decreasing manipulated variable determiner 26 e.

In the first embodiment described above, Kmu_att has always been set to1 in the case where the determination result in S122-5-1 is affirmative,i.e., the updating cancellation condition does not apply. In contrastthereto, according to the present embodiment, Kmu_att is set such thatKmu_att changes within a range from 0 to 1 according to Mnsp_estm andMnsp_sens as illustrated in, for example, FIG. 14 in the case where thedetermination result in S122-5-1 is affirmative.

FIG. 14 visually illustrates the set values of Kmu_att corresponding topairs of the values of Mnsp_estm and the values of Mnsp_sens on acoordinate plane, Mnsp_estm being on the axis of abscissas and Mnsp_sensbeing on the axis of ordinates. In the diagram, the numeral values 0(excluding 0 at the intersection (the point of origin) of the axis ofordinates and the axis of abscissas, 0.5, and 1 indicate therepresentative examples of set values of Kmu_att. In the example givenin FIG. 14, Kmu_att is always set to zero in the case where the point ofthe pair of the value of Mnsp_estm and the value of Mnsp_sens(Mnsp_estm, Mnsp_sens lies in a second quadrant (the range whereinMnsp_estm<0 and Mnsp_sens>0) or a fourth quadrant (Mnsp_estm>0 andMnsp_sens<0), i.e., Mnsp_estm and Mnsp_sens have polarities oppositefrom each other.

Further, if a point (Mnsp_estm, Mnsp_sens) falls in a first quadrant(the range wherein Mnsp_estm>0 and Mnsp_sens>0), Kmu_att is set to 0,0.5, or 1, respectively, when the point (Mnsp_estm, Mnsp_sens) lies on ahalf line L02 a or L04 a, a half line L12 a or L14 a, or a half line L22a or L24 a, respectively.

Further, Kmu_att is always set to 0 in the range between the half linesL02 a, L04 a and the axis of ordinates and the axis of abscissas in thefirst quadrant.

Further, Kmu_att is always set to 1 in the range above the half line L24a, in which Mnsp_sens is larger, and on the right to the half line L22a, in which Mnsp_estm is larger in the first quadrant.

In the range between the half lines L02 a and L22 a, if the value ofMnsp_sens is fixed, then Kmu_att is set such that Kmu_att continuouslychanges between 0 and 1 according to Mnsp_estm.

Similarly, in the range between the half lines L04 a and L24 a, if thevalue of Mnsp_estm is fixed, then Kmu_att is set such that Kmu_attcontinuously changes between 0 and 1 according to Mnsp_sens.

Further, if a point (Mnsp_estm, Mnsp_sens) falls in a third quadrant (arange wherein Mnsp_estm<0 and Mnsp_sens<0), then Kmu_att is set to beorigin-symmetrical to Kmu_att set in the first quadrant.

More specifically, Kmu_att is set such that, if Kmu_att is defined as afunction of Mnsp_estm and Mnsp_sens and represented asKmu_att=f_kmuatt(Mnsp_estm, Mnsp_sens), then Kmu_att in the thirdquadrant will be Kmu_att=f_kmuatt(−Mnsp_estm, −Mnsp_sens). In this case,the half lines L02 b, L12 b, L22 b, L04 b, L14 b, and L24 b in the thirdquadrant of FIG. 14 correspond to the half lines L02 a, L12 a, L22 a,L04 a, L14 a, and L24 a, respectively, in the first quadrant.

The frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e in the present embodiment carries out the processingillustrated by, for example, the flowchart of FIG. 15 thereby todetermine the road surface frictional coefficient increasing/decreasingmanipulated variable Δμ while setting Kmu_att as described above. InFIG. 15, for the same processing as the processing illustrated by theflowchart of FIG. 13 in the first embodiment, the same referencecharacters as those in FIG. 13 are used.

The frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e first carries out the same determination processing inS122-5-1 as that in the first embodiment. If the determination result inS122-5-1 is positive (i.e., if the updating cancellation condition doesnot apply), then the frictional coefficient increasing/decreasingmanipulated variable determiner 26e carries out the processing ofS122-5-6 to S122-5-10 so as to set the value of the gain adjustmentparameter Kmu_att. If the determination result is negative (i.e., if theupdating cancellation condition applies), then the frictionalcoefficient increasing/decreasing manipulated variable determiner 26 esets the value of the gain adjustment parameter Kmu_att to 0 inS122-5-3.

In the aforesaid processing from S122-5-6 to 5122-5-10, the frictionalcoefficient increasing/decreasing manipulated variable determiner 26 efirst determines in S122-5-6 the value of a parameter w1 by theexpression shown in the flowchart on the basis of the absolute value ofMnsp_estm (a b s(Mnsp_estm)).

The parameter w1 defines the form of changes in Kmu_att based on theabsolute value of Mnsp_estm when the value of Mnsp_sens is fixed. Inthis case, in the example of setting Kmu_att in the present embodimentas illustrated in FIG. 14, C1 and C2 in the expression of S122-5-6 areset to predetermined positive values beforehand.

Subsequently, in S122-5-7, the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e determinesthe value of a parameter w2 as a first candidate value of Kmu_att by theexpression given in the flowchart on the basis of the value of w1 andthe absolute value Mnsp_sens (a b s(Mnsp_sens)).

In this case, in the example for setting Kmu_att in the presentembodiment as illustrated in FIG. 14, C3 in the expression of S122-5-7is set to a predetermined negative value beforehand. The relationshipbetween Mnsp_estm and Mnsp_sens when the value of w2 is set to 0 or 0.5or 1 in the expression of S122-5-7 will be the relationship betweenMnsp_estm and Mnsp_sens on the half lines L02 a, L02 b or the half linesL12 a, L12 b, or the half lines L22 a, L22 b in FIG. 14.

Subsequently, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e determines in S122-5-8 the value ofa parameter w3 by the expression shown in the flowchart on the basis ofthe absolute value of Mnsp_sens (a b s (Mnsp_sens)). The parameter w3defines the form of changes in Kmu_att based on the absolute value ofMnsp_sens when the value of Mnsp_estm is fixed. In this case, in theexample of setting Kmu_att in the present embodiment as illustrated inFIGS. 14, C4 and C5 in the expression of S122-5-8 are set topredetermined positive values beforehand.

Subsequently, in S122-5-9, the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e determinesthe value of a parameter w4 as a second candidate value of Kmu_att bythe expression given in the flowchart on the basis of the value of w3and the absolute value of Mnsp_estm (a b s(Mnsp_estm)). In this case, inthe example for setting Kmu_att in the present embodiment as illustratedin FIG. 14, C6 in the expression of S122-5-9 is set to a predeterminednegative value beforehand.

The relationship between Mnsp_estm and Mnsp_sens when the value of w4 isset to 0 or 0.5 or 1 in the expression of S122-5-9 will be therelationship between Mnsp_estm and Mnsp_sens on the half lines L04 a,L04 b or the half lines L14 a, L14 b, or the half lines L24 a, L24 b.

Subsequently, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e determines Kmu_att in 5122-5-10 bythe expression in the flowchart.

The value of Kmu_att in the first quadrant and the third quadrant of thecoordinate plane shown in FIG. 14 will be set as illustrated in thediagram by carrying out the processing in S122-5-6 to S122-5-10 asdescribed above.

In the present embodiment, the processing in S122-5-1, S122-5-3, andS122-5-6 to S122-5-10 described above is the processing carried out bythe gain adjuster in FIG. 11.

The present embodiment is the same as the first embodiment except forthe aspects described above. According to the present embodiment, asdescribed above, in the case where the road surface frictionalcoefficient estimated value μ_estm is updated according to Mnsp_err bysetting the value of Kmu_att (i.e., in the case where the updatingcancellation condition does not apply), if the Mnsp_sens or Mnsp_estm isrelatively close to zero, then the magnitude of the frictionalcoefficient operation gain Gmu decreases as the Mnsp_sens or Mnsp_estmapproaches to zero. As a result, the absolute value of the updatingamount of the road surface frictional coefficient estimated valueμ_estm, i.e., the frictional coefficient increasing/decreasingmanipulated variable Δμ, is restrained to be small.

This arrangement makes it possible to restrain improper updating of theroad surface frictional coefficient estimated value μ_estm as Mnsp_sensor Mnsp_estm approaches zero, causing the error of Mnsp_sens orMnsp_estm to easily become relatively large with respect to themagnitude of the actual NSP yaw moment Mnsp_act.

Third Embodiment

A third embodiment of the present invention will now be described withreference to FIG. 16. The present embodiment differs from the aforesaidsecond embodiment only in the method for setting the gain adjustmentparameter Kmu_att in the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e.

More specifically, the present embodiment considers not only thepolarities of an NSP yaw moment estimated value Mnsp_estm and an NSP yawmoment detected value Mnsp_sens but also the polarity of a μ sensitivityp (γ_sens, δf_sens, Vgx_estm). Further, if a predetermined updatingcancellation condition including at least a condition related to thepolarities applied, then updating of the road surface frictionalcoefficient estimated value μ_estm according to a yaw moment estimationerror Mnsp_err is cancelled.

Here, as is obvious from the aforesaid expression 4-13b, the μsensitivity p indicative of the ratio of an increment of an actual NSPyaw moment Mnsp_act in response to an increment of an actual roadsurface frictional coefficient μ_act should have the same polarity asthat of the actual NSP yaw moment Mnsp_act.

Hence, in the present embodiment, if the polarity of any one ofMnsp_estm, Mnsp_sens, and p is different from those of the remaining twopolarities, then it is decided that the updating cancellation conditionapplies, and the updating of μ_estm according to Mnsp_err is cancelled.

To be more specific, according to the present embodiment, a frictionalcoefficient increasing/decreasing manipulated variable determiner 26 ecarries out the processing illustrated by the flowchart of FIG. 16 so asto determine a frictional coefficient increasing/decreasing manipulatedvariable Δμ. In FIG. 16, the same processing steps as those in theflowchart of FIG. 15 in the second embodiment are assigned the samereference characters as those in FIG. 15.

According to the processing illustrated by the flowchart of FIG. 16, thedetermination processing in S122-5-20 is carried out in place of thedetermination processing in S122-5-1 of FIG. 15 in the secondembodiment. The rest of the processing is the same as that of the secondembodiment.

In this case, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e determines in the determinationprocessing in S122-5-20 whether a condition that Mnsp_estm>Mm andMnsp_sens>Ms and p>p0 or a condition that Mnsp_estm<−Mm andMnsp_sens<−Ms and p<−p0 applies. Here, the Mm, Ms and p0 denotenon-negative predetermined values (zero or positive values in thevicinity of zero), which are set beforehand.

In the present embodiment, if the determination result in S122-5-20 isnegative, then it means that the updating cancellation conditionapplies. In this case, if the predetermined values of Mm, Ms and p0 havebeen set to zero, then a negative determination result in S122-5-20(i.e., the updating cancellation condition applies) is equivalent to thepolarity of one of Mnsp_estm, Mnsp_sens and p being different from thepolarities of the remaining two.

Meanwhile, if the predetermined values Mm, Ms and p0 have been set topositive values, then the determination result in S122-5-20 will benegative (the updating cancellation condition applies) not only in thecase where the polarity of one of Mnsp_estm, Mnsp_sens, and p isdifferent from the polarities of the remaining two but also in the casewhere −Mm≦Mnsp_estm≦Mm or —Ms≦Mnsp_sens≦Ms or −p0≦p≦p0 holds (in otherwords, in the case where one of Mnsp_estm, Mnsp_sens and p takes a valuein a range in the vicinity of zero).

In this case, therefore, the updating cancellation condition includes acondition that p has a polarity opposite from at least one of Mnsp_estmand Mnsp_sens and a condition that one of Mnsp_estm, Mnsp_sens and ptakes a value within a predetermined range in the vicinity of zero, inaddition to the condition that Mnsp_estm and Mnsp_sens have polaritiesopposite from each other.

In the present embodiment, the function of the updating cancellationcondition determiner in the present invention is implemented by thedetermination processing in the aforesaid S122-5-20. The same applies toa fourth to the eighth embodiments, which will be discussed hereinafter.

The present embodiment is the same as the second embodiment except forthe aspects described above.

In the present embodiment, the processing in S122-5-20, S122-5-3, andS122-5-6 to S122-5-14 is the processing carried out by the gain adjustorin FIG. 11. In this case, the polarity of the μ sensitivity p is takeninto account, so that the μ sensitivity p is input to the gain adjustor,as indicated by the dashed-line arrow in the figure.

In the present embodiment, updating the μ_estm on the basis of Mnsp_erris cancelled in the case where the polarity of one of Mnsp_estm,Mnsp_sens and p is different from the polarities of the remaining two.This makes it possible to further securely prevent μ_estm fromdiverting.

Further, in the case where the predetermined values Mm, Ms and p0 havebeen set to positive values, if Mnsp_sens or Mnsp_estm or p takes avalue within a range in the vicinity of zero, then the determinationresult in S122-5-20 becomes negative. This causes the value of Δμ to beforcibly set to zero. Thus, updating the μ_estm on the basis of Mnsp_errcan be cancelled also in the case where the error of Mnsp_sens orMnsp_estm or p is apt to become relatively large, as compared with themagnitude of the actual NSP yaw moment Mnsp_act.

Fourth Embodiment

A fourth embodiment of the present invention will now be described withreference to FIG. 17. The present embodiment differs from the thirdembodiment described above only in the method for setting the gainadjustment parameter Kmu_att in a frictional coefficientincreasing/decreasing manipulated variable determiner 26 e.

In the aforesaid third embodiment, if the determination result inS122-5-20 is affirmative (in the case where the updating cancellationcondition does not apply), then the road surface frictional coefficientestimated value μ_estm has always been updated according to an NSP yawmoment error Mnsp_err. In contrast thereto, according to the presentembodiment, if the determination result in S122-5-20 is negative (in thecase where the updating cancellation condition applies), thenthereafter, μ_estm is updated according to Mnsp_err only if thedetermination result in S122-5-20 remains to be affirmative (theupdating cancellation condition does not apply) continuously for apredetermined period of time or more.

In other words, according to the present embodiment, once the updatingcancellation condition has been applied, then a state wherein theupdating cancellation condition does not apply is required to last forthe predetermined period of time or more before the μ_estm is allowed tobe updated on the basis of Mnsp_err.

To be more specific, in the present embodiment, a frictional coefficientincreasing/decreasing manipulated variable determiner 26 e carries outthe processing illustrated in the flowchart of FIG. 17 to determine thefrictional coefficient increasing/decreasing manipulated variable Δμ. InFIG. 17, the same processing steps as those illustrated by the flowchartof FIG. 16 in the third embodiment are assigned the same referencecharacters as those in FIG. 16.

The frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e first carries out in S122-5-20 the same determinationprocessing (processing for determining whether an updating cancellationcondition applies) as that in the third embodiment.

If the determination result of S122-5-20 is negative (if the updatingcancellation condition applies), then the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e sets, inS122-5-21, the value on a countdown timer TM to an initial value Twaitdetermined in advance and then carries out the determination processingin S122-5-22.

If the determination result of S122-5-20 is affirmative (if the updatingcancellation condition does not apply), then the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e directlycarries out the determination processing in S122-5-22.

In the aforesaid determination processing in 5122-5-22, the frictionalcoefficient increasing/decreasing manipulated variable determiner 26 edetermines whether the current value on the countdown timer TM is zeroor less (whether the counting of time equivalent to the aforesaidinitial value Twait has been completed).

If the determination result of S122-5-22 is affirmative, then thefrictional coefficient increasing/decreasing manipulated variabledeterminer 26 e carries cut the processing of S122-5-6 to S122-5-14described in the second embodiment, thereby setting the value of a gainadjustment parameter Kmu_att.

Meanwhile, if the determination result of S122-5-22 is negative, thenthe frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e decrements in S122-5-23 the value on the countdown timerTM by the time equivalent to an arithmetic processing cycle ΔT.

Further, the frictional coefficient increasing/decreasing manipulatedvariable determiner 26 e sets the value of the gain adjustment parameterKmu_att to zero in S122-5-24.

Subsequently, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e carries out in S122-5-4 the sameprocessing as that in the second embodiment so as to determine thefrictional coefficient increasing/decreasing manipulated variable Δμ.

According to the processing described above, once the determinationresult in S122-5-20 turns to be negative (once the updating cancellationcondition applies), then the value of the gain adjustment parameterKmu_att is set to zero even if the determination result in S122-5-20 isaffirmative until the state wherein the determination result inS122-5-20 is affirmative (the state wherein the updating cancellationcondition does not apply) continues for not less than predetermined timespecified by the initial value Twait of the countdown timer TM. Thus,the state wherein the updating of μ_estm according to Mnsp_err iscancelled is maintained.

Then, updating μ_estm on the basis of Mnsp_err is resumed in the casewhere the state in which the determination result in S122-5-20 isaffirmative (the state wherein the updating cancellation condition doesnot apply) continues for not less than the predetermined time specifiedby the initial value Twait of the countdown timer TM.

The present embodiment is the same as the aforesaid third embodimentexcept for the aspects described above. According to the presentembodiment, if the state wherein the updating cancellation conditionapplies is changed over to the state wherein the updating cancellationcondition does not apply, then updating μ_estm according Mnsp_err isprohibited during a period immediately following the changeover (aperiod equivalent to the time of the initial value Twait). Thisarrangement makes it possible to prevent the road surface frictionalcoefficient estimated value μ_estm from being updated to an impropervalue if the state wherein the updating cancellation condition does nottemporarily apply is accidentally set due to an influence of adisturbance or the like.

In the third embodiment and the fourth embodiment described above, inthe case where the determination result in S122-5-20 is affirmative (inthe case where the updating cancellation condition does not apply), thegain adjustment parameter Kmu_att has been determined by the processingin S122-5-6 to S122-5-14 in the second embodiment. Alternatively,however, the value of Kmu_att may be set to 1 as with the firstembodiment in the case where the determination result in S122-5-20 isaffirmative (in the case where the updating cancellation condition doesnot apply).

Further, the updating cancellation condition in the fourth embodiment isthe same as that in the third embodiment. Alternatively, however, thefourth embodiment may use the same updating cancellation condition asthat in the first embodiment and the second embodiment. In other words,in the fourth embodiment, the determination processing in S122-5-1 maybe carried out instead of the determination processing in S122-5-20.

In the first to the fourth embodiments, in the case where the updatingcancellation condition applies (in the case where the determinationresult in S122-5-1 or 5122-5-20 is negative), the frictional coefficientincreasing/decreasing manipulated variable Δμ may be set to zero withoutusing the value of the gain adjustment parameter Kmu_att. Alternatively,the value of Δμ may be set to a predetermined positive value, which hasbeen decided beforehand, in place of setting the frictional coefficientincreasing/decreasing manipulated variable 4 to zero, and the roadsurface frictional coefficient estimated value μ_estm may be graduallyincreased at a certain temporal incremental rate in the state whereinthe updating cancellation condition applies.

Fifth Embodiment

Referring now to FIG. 18, a fifth embodiment of the present inventionwill be described. The present embodiment differs from the thirdembodiment or the fourth embodiment only partly in the processingcarried out by a μ estimator 26.

To be more specific, in the present embodiment, the μ estimator 26 has asaturation characteristic element 26 g to which a μ sensitivity p(γ_sens, δf_sens, Vgx_estm) calculated by the aforesaid μ sensitivitycalculator 26 d is supplied. The saturation characteristic element 26 ggenerates an output (a function value of the μ sensitivity p) having asaturation characteristic relative to the μ sensitivity p that is input.Hereinafter, the output will be referred to as a μ-sensitivity-dependentvalue p_a.

In this case, a relationship between the μ sensitivity p and theμ-sensitivity-dependent value p_a is set beforehand in the form of mapdata or an arithmetic expression.

More specifically, the relationship between the μ sensitivity p and theμ-sensitivity-dependent value p_a is set such that if p is zero, thenp_a is also zero and p_a monotonically increases as p increases and themagnitude of the change rate with respect to an increase in p (a valueobtained by differentiating p_a by p) decreases (the value of p_agradually saturates) as the absolute value of p increases.

A frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e of the μ estimator 26 in the present embodiment uses theμ-sensitivity-dependent value p_a instead of the μ sensitivity p tocalculate the right side of the aforesaid expression 7-2 so as todetermine a frictional coefficient increasing/decreasing manipulatedvariable Δμ in the processing in the aforesaid

S122-5-4. In other words, Δμ is determined by the calculation ofexpression 7-2a given below.

$\begin{matrix}\begin{matrix}{{\Delta\mu} = {{Mnsp\_ err}*{Gmu}}} \\{= {{Mnsp\_ err}*\left( {{p\_ a}*{Kmu}*{Kmu\_ att}} \right)}}\end{matrix} & {{Expression}\mspace{14mu} 7\text{-}2a}\end{matrix}$

The present embodiment is the same as the third embodiment or the fourthembodiment except for the aspects described above. Thus, according tothe present embodiment, in the case where the frictional coefficientincreasing/decreasing manipulated variable Δμ is determined on the basisof Mnsp_err (in the case where the determination result in S122-5-20 isaffirmative or the determination results in S122-5-20 and S122-5-22 areaffirmative), the value of Δμ is determined such that Δμ is proportionalto the product of Mnsp_err and the μ-sensitivity-dependent value p_a.

In the determination processing of S122-5-20, namely, the processing fordetermining whether the updating cancellation condition applies, theμ-sensitivity-dependent value p_a may be used instead of the μsensitivity p to carry out the determination processing.

In determining the frictional coefficient increasing/decreasingmanipulated variable Δμ on the basis of Mnsp_err, the present embodimentrestrains the magnitude of a frictional coefficient operation gain Gmu(feedback gain) from becoming excessively large when the absolute valueof the μ sensitivity p is large. As a result, it is possible to preventa road surface frictional coefficient estimated value μ_estm calculatedby the μ estimator 26 from unstably fluctuating or vibrating.

Supplementally, determining the frictional coefficientincreasing/decreasing manipulated variable Δμ by using theμ-sensitivity-dependent value p_a as in the present embodiment can beapplied also to the first embodiment or the second embodiment describedabove. In this case, the processing in S122-5-4 (the processing forcalculating Δμ in the case where the updating cancellation conditiondoes not apply) in the first embodiment or the second embodiment maycarry out the computation of the aforesaid expression 7-2a to determinethe frictional coefficient increasing/decreasing manipulated variableΔμ.

Sixth Embodiment

A sixth embodiment of the present invention will now be described withreference to FIG. 19. The present embodiment differs from the third orthe fourth embodiment only partly in the processing carried out by a μestimator 26.

To be more specific, according to the present embodiment, the μestimator 26 has frequency component regulating filters 26 ba, 26 aa,and 26 da which receive the NSP yaw moment estimated value Mnsp_estmcalculated by the aforesaid Mnsp_estm calculator 26 b, the NSP yawmoment dv Mnsp_sens calculated by the aforesaid Mnsp_sens calculator 26a, and the μ sensitivity p (γ_sens, δf_sens, Vgx_estm) calculated by theaforesaid η sensitivity calculator 26 d, respectively, and thesaturation characteristic element 26 g described in the fifth embodimentdescribed above.

In this example, all the filters 26 ba, 26 aa, and 26 da have a low-cutcharacteristic, which cuts off low-frequency components of apredetermined frequency or lower. More specifically, the transferfunctions of the filters 26 ba, 26 aa, and 26 da are represented by, forexample, Ta*S/(1+Ta*S). In other words, the frequency characteristics ofthe filters 26 ba, 26 aa, and 26 da are set to share the same targetcharacteristic, namely, a low-cut characteristic (set to share the sametransfer function time constant Ta).

If a phase disagreement between Mnsp_err and p or a phase disagreementbetween Mnsp_sens and Mnsp_estm takes place in a state wherein μ_estmand μ_act are in accurate agreement due to, for example, differentfrequency characteristics or the like of the sensors used to generateinput values of the filters 26 ba, 26 aa, and 26 da, then the frequencycharacteristics of the filters 26 ba, 26 aa, and 26 da may be shiftedfrom each other to resolve the phase disagreement.

Further, according to the present embodiment, the μ estimator 26calculates, by an Mnsp_err calculator 26 c, an NSP yaw moment filteringestimation error Mnsp_err_f (=Mnsp_sens_f−Mnsp_estm_f) in place of thedifference between Mnsp_sens and Mnsp_estm (the NSP yaw momentestimation error). The NSP yaw moment filtering estimation errorMnsp_err_f is the difference between an NSP yaw moment filteringdetected value Mnsp_sens_f, which is an output of the filter 26 aa towhich Mnsp_sens is input, and an NSP yaw moment filtering estimatedvalue Mnsp_estm_f, which is an output of the filter 26 ba to whichMnsp_estm is input.

In the present embodiment, the frequency characteristics of the filters26 aa and 26 ba are the same, so that determining the differenceMnsp_err_f between Mnsp_sens_f and Mnsp_estm_f as described above isequivalent to determining Mnsp_err_f by passing the NSP yaw moment errorMnsp_err, which is the difference between Mnsp_sens and Mnsp_estm,through a filter having the same frequency characteristics of thefilters 26 aa and 26 ba.

Therefore, a filter which receives Mnsp_err and which has the samefrequency characteristic as those of the filters 26 aa and 26 ba may beprovided so as to obtain Mnsp_err_f by passing Mnsp_err through thefilter.

The μ estimator 26 determines a μ-sensitivity-dependent value p_fa asthe function value of p_f by inputting the μ sensitivity filtering valuep_f, which is an output of the filter 26 da receiving the μ sensitivityp, in place of the μ sensitivity p to the aforesaid saturationcharacteristic element 26 g. In this case, the relationship between p_fand p_fa is the same as the relationship between an input (p) and anoutput (p_a) of the saturation characteristic element 26 g described inthe aforesaid fifth embodiment.

Alternatively, the μ-sensitivity-dependent value p_fa may be determinedby supplying an output (p_a), which has been obtained by passing the IAsensitivity p through the saturation characteristic element 26 g, to thefilter 26 da.

Subsequently, a frictional coefficient increasing/decreasing manipulatedvariable determiner 26 e of the μ estimator 26 in the present embodimentuses Mnsp_sens_f, Mnsp_estm_f and p_f, which are the filtering values ofMnsp_sens, Mnsp_estm and p, respectively, in place of Mnsp_sens,Mnsp_estm and p to carry out the determination processing in S122-5-20,thereby determining whether the updating cancellation condition applies.

In this determination processing, instead of the μ sensitivity filteringvalue p_f, the μ-sensitivity-dependent value p_fa obtained by passingthe μ sensitivity p through both the filter 26 da and the saturationcharacteristic element 26 g may be used.

Further, the frictional coefficient increasing/decreasing manipulatedvariable determiner 26 e of the μ estimator 26 in the present embodimentuses the NSP yaw moment filtering estimation error Mnsp_err_f and theμ-sensitivity-dependent value p_fa in place of NSP yaw moment estimationerror Mnsp_err and the μ sensitivity p, respectively, to calculate theright side of the aforesaid expression 7-2, thereby determining thefrictional coefficient increasing/decreasing manipulated variable Δμ inthe processing in S122-5-4. In other words, Δμ is determined accordingto expression 7-2b given below.

$\begin{matrix}\begin{matrix}{{\Delta\mu} = {{Mnsp\_ err}{\_ f}*{Gmu}}} \\{= {{Mnsp\_ err}{\_ f}*\left( {{p\_ fa}*{Kmu}*{Kmu\_ att}} \right)}}\end{matrix} & {{Expression}\mspace{14mu} 7\text{-}2b}\end{matrix}$

The present embodiment is the same as the third or the fourth embodimentexcept for the aspects described above. Thus, according to the presentembodiment, in the case of determining the frictional coefficientincreasing/decreasing manipulated variable Δμ on the basis of Mnsp_err(in the case where the determination result in S122-5-20 is affirmativeor the determination results in S122-5-20 and S122-5-22 areaffirmative), the value of Δμ is determined on the basis of the NSP yawmoment filtering estimation error Mnsp_err_f and the μ sensitivityfiltering value p_f (more specifically, such that the value of Δμ isproportional to the product of the Mnsp_err_f and theμ-sensitivity-dependent value p_fa).

In the present embodiment, the filters 26 ba, 26 aa, and 26 dacorrespond to a first filter, a second filter, and a third filter,respectively, in the present invention. Further, the NSP yaw momentfiltering estimated value Mnsp_estm_f corresponds to a first estimatedfiltering value in the present invention and the NSP yaw momentfiltering detected value Mnsp_sens_f corresponds to a second estimatedfiltering value.

According to the present embodiment, determining the frictionalcoefficient increasing/decreasing manipulated variable Δμ by using theNSP yaw moment filtering estimation error Mnsp_err_f and theμ-sensitivity-dependent value p_fa obtained using the filters 26 ba, 26aa, and 26 da having the low-cut characteristics makes it possible todetermine the road surface frictional coefficient estimated value μ_estmwhile removing unwanted components included in Mnsp_lens, Mnsp_estm, andp attributable to a steady offset or drift of an output of sensors, suchas a yaw rate sensor 13 and a lateral acceleration sensor 15, or anactual road surface bank angle θbank_act. This permits higher accuracyof μ_estm.

Supplementally, determining the frictional coefficientincreasing/decreasing manipulated variable Δμ by using the NSP yawmoment filtering estimation error Mnsp_err_f and theμ-sensitivity-dependent value p_fa as in the present embodiment can beapplied also to the first or the second embodiment described above.

In this case, the processing in S122-5-4 (the processing for calculatingΔμ in the case where the updating cancellation condition does not apply)in the first or the second embodiment described above may carry out thecomputation of the aforesaid expression 7-2b so as to determine thefrictional coefficient increasing/decreasing manipulated variable Δμ.

Further, regarding the determination processing related to the updatingcancellation condition, when carrying out the determination processingin S122-5-1, Mnsp_lens_f and Mnsp_estm_f may be used in place ofMnsp_sens and Mnsp_estm to perform the determination processing.

Further, in the present embodiment, the μ sensitivity p has been passedthrough both the filter 26 da and the saturation characteristic element26 g. However, if the magnitude of the μ sensitivity p is not expectedto increase much, then the saturation characteristic element 26 g may beomitted. In this case, the processing in S122-5-4 may calculate thefrictional coefficient increasing/decreasing manipulated variable Δμaccording to an expression which has replaced p_fa of the right side ofthe aforesaid expression 7-2b by the μ sensitivity filtering value p_f.

Further alternatively, of the filters 26 ba, 26 aa, and 26 da, thefilters 26 ba and 26 aa related to the NSP yaw moment estimated valueand detected value may be omitted, or the filter 26 da related to the μsensitivity p may be omitted.

Seventh Embodiment

A seventh embodiment of the present invention will now be described withreference to FIG. 20. The present embodiment differs from the third orthe fourth embodiment only partly in the processing carried out by theaforesaid μ estimator 26.

To be more specific, a μ estimator 26 in the present embodiment hasfilters 26 bb, 26 ab, and 26 db, which have different frequencycharacteristics from those of the filters 26 ba, 26 aa, and 26 dadescribed in the aforesaid sixth embodiment. The NSP yaw momentestimated value Mnsp_estm calculated by the aforesaid Mnsp_estmcalculator 26 b, an NSP yaw moment detected value Mnsp_sens, the NSP yawmoment detected value Mnsp_sens calculated by the aforesaid Mnsp_senscalculator 26 a, and a μ sensitivity p (γ_sens, δf_sens, Vgx_estm)calculated by the aforesaid μ sensitivity calculator 26 d are input tothe filters 26 bb, 26 ab, and 26 db, respectively.

In this example, all the filters 26 bb, 26 ab, and 26 db have a high-cutcharacteristic (characteristic that cuts off high-frequency componentsof a predetermined frequency or higher). More specifically, the transferfunctions of the filters 26 bb, 26 ab, and 26 db are represented by, forexample, 1/(1+Tb*S).

In other words, the frequency characteristics of the filters 26 bb, 26ab, and 26 db are set to share the same target characteristic, namely, ahigh-cut characteristic (set to share the same transfer function timeconstant Tb). In other words, the frequency characteristics of thefilters 26 bb, 26 ab, and 26 db are low-pass characteristics. If a phasedisagreement between Mnsp_err and p or a phase disagreement betweenMnsp_sens and Mnsp_estm takes place in a state wherein μ_estm and 82_act are in accurate agreement due to different frequencycharacteristics or the like of the sensors used to generate input valuesof the filters 26 bb, 26 ab, and 26 db, then the frequencycharacteristics of the filters 26 bb, 26 ab, and 26 db may be shiftedfrom each other to resolve the phase disagreement. The frequencycharacteristics of the filters 26 bb, 26 ab, and 26 db may be those ofband-pass filters as long as they have the high-cut characteristicsrather than being limited to the low-pass characteristics.

Further, according to the present embodiment, the μ estimator 26calculates, by an Mnsp_err calculator 26 c, an NSP yaw moment filteringestimation error Mnsp_err_f (=Mnsp_sens_f−Mnsp_estm_f) in place of thedifference between Mnsp_sens and Mnsp_estm (the NSP yaw momentestimation error Mnsp_err). The NSP yaw moment filtering estimationerror Mnsp_err_f is the difference between an NSP yaw moment filteringdetected value Mnsp_sens_f, which is an output of the filter 26 ab towhich Mnsp_sens is input, and an NSP yaw moment filtering estimatedvalue Mnsp_estm_f, which is an output of the filter 26 bb to whichMnsp_estm is input.

As with the case described in the sixth embodiment, the NSP yaw momentestimation error Mnsp_err, which is the difference between Mnsp_sens andMnsp_estm, may be passed through a filter having the same frequencycharacteristic (high-cut characteristic) as those of the filters 26 baand 26 aa thereby to obtain Mnsp_err_f.

The μ estimator 26 in the present embodiment further has a saturationcharacteristic element 26 g described in the aforesaid fifth embodiment.The μ estimator 26 passes the μ sensitivity filtering value p_f, whichis an output of the filter 26 db receiving the μ sensitivity p, in placeof the μ sensitivity p through the saturation characteristic element 26g to determine the μ-sensitivity-dependent value p fa as the functionvalue of p_f, as with the sixth embodiment described above. An output(p_a) obtained by passing the μ sensitivity p through the saturationcharacteristic element 26 g may be passed through the filter 26 db todetermine the μ-sensitivity-dependent value p_fa.

As with the sixth embodiment, in the aforesaid determination processingin S122-5-20, the frictional coefficient increasing/decreasingmanipulated variable determiner 26 e of the μ estimator 26 in thepresent embodiment uses Mnsp_sens_f, Mnsp_estm_f and p_f, which are thefiltering values of Mnsp_sens, Mnsp_sens and p, to carry out thedetermination processing to determine whether the updating cancellationcondition applies.

In the determination processing, the μ-sensitivity-dependent value p_faobtained by passing the μ sensitivity p through both the filter 26 daand the saturation characteristic element 26 g may be used in place ofthe μ sensitivity filtering value p_f.

Further, the frictional coefficient increasing/decreasing manipulatedvariable determiner 26 e of the μ estimator 26 in the present embodimentdetermines the frictional coefficient increasing/decreasing manipulatedvariable Δμ as described below by carrying out the processing inS122-5-4.

The frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e first multiplies the aforesaid NSP yaw moment filteringestimation error Mnsp_err_f by the μ-sensitivity-dependent value p_faand the basic gain Kmu to determine a preliminary value μ_a of thefrictional coefficient increasing/decreasing manipulated variable Δμ.More specifically, the value determined by an expression in which thevalue of Kmu_att of the right side of the aforesaid expression 7-2b is 1is obtained as the preliminary value Δμ_a.

In the present embodiment, the filters 26 bb, 26 ab, and 26 db have thehigh-cut characteristics, so that a phase delay in the NSP yaw momentfiltering estimation error Mnsp_err_f or the μ-sensitivity-dependentvalue p_fa (or the μ sensitivity filtering value p_f) is apt to occur ina relatively high-frequency range, frequently causing a phase delay inthe preliminary value Δμ_a determined as described above. For thisreason, if the Δμ_a were used as it is to update the road surfacefrictional coefficient estimated value μ_estm, then the μ_estm would belikely to vibrate.

According to the present embodiment, therefore, the frictionalcoefficient increasing/decreasing manipulated variable determiner 26 eis provided with a phase compensation element 26 ea for advancing thephase of the preliminary value Δμ_a to correct a phase delay. Thetransfer function of the phase compensation element 26 ea is representedby (1+Tb*s)/(1+Tc*S). The time constant Tb of the numerator is the sameas the time constant Tb of the denominator of the transfer functionrepresenting the filters 26 bb, 26 ab, and 26 db.

Then, the frictional coefficient increasing/decreasing manipulatedvariable determiner 26 e in the present embodiment passes thepreliminary value Δμ_a determined as described above through the phasecompensation element 26 ea and further multiplies the output of thephase compensation element 26 ea by the gain adjustment parameterKmu_att so as to determine a final frictional coefficientincreasing/decreasing manipulated variable Δμ (a current value).

Thus, the value of Δμ is determined on the basis of the NSP yaw momentfiltering estimation error Mnsp_err_f and the μ sensitivity filteringvalue p_f (more specifically, the product of Mnsp_err_f and theμ-sensitivity-dependent value p_fa).

Alternatively, the product of the NSP yaw moment filtering estimationerror Mnsp_err_f and the μ-sensitivity-dependent value p_may bedetermined as the preliminary value Δμ_a, and then the output of thephase compensation element 26 ea obtained by passing the preliminaryvalue Δμ_a through the phase compensation element 26 ea may bemultiplied by the basic gain Kmu and the gain adjustment parameterKmu_att, thereby determining the frictional coefficientincreasing/decreasing manipulated variable Δμ (a current value).

Further alternatively, the result obtained by multiplying Mnsp_err_f bythe μ-sensitivity-dependent value p_fa, the basic gain Kmu, and the gainadjustment parameter Kmu_att may be determined as the preliminary valueΔμ_a, and the preliminary value Δμ_a may be passed through the phasecompensation element 26 ea so as to determine the frictional coefficientincreasing/decreasing manipulated variable Δμ (a current value).

The present embodiment is the same as the third or the fourth embodimentexcept for the aspects described above.

In the present embodiment, the filters 26 bb, 26 ab, and 26 dbcorrespond to the first filter, the second filter, and the third filter,respectively, in the present invention. The NSP yaw moment filteringestimation value Mnsp_estm_f corresponds to a first estimated filteringvalue in the present invention, and the NSP yaw moment filteringdetected value Mnsp_sens_f corresponds to a second estimated filteringvalue in the present invention.

In the present embodiment, the NSP yaw moment filtering estimation errorMnsp_err_f and the μ-sensitivity-dependent value p_fa obtained by usingthe filters 26 bb, 26 ab, and 26 db having the high-cut characteristicsare used to determine the frictional coefficient increasing/decreasingmanipulated variable Δμ.

This arrangement makes it possible to determine the road surfacefrictional coefficient estimated value μ_estm, removing unwantedcomponents included in Mnsp_sens, Mnsp_estm, and p due to high-frequencynoises contained in the outputs of sensors, such as a yaw rate sensor 13and a lateral acceleration sensor 15. As a result, the accuracy ofμ_estm can be enhanced.

Furthermore, correcting the phase delay of Δμ by the phase compensationelement 26 ea prevents μ_estm determined by the μ estimator 26 fromvibrating. This permits enhanced robustness of the processing forestimating the road surface frictional coefficient μ.

Supplementally, determining the frictional coefficientincreasing/decreasing manipulated variable Δμ by using the NSP yawmoment filtering estimation error Mnsp_err_f and theμ-sensitivity-dependent value p_fa as in the present embodiment can beapplied also to the first or the second embodiment described above.

In this case, the processing in S122-5-4 (the processing for calculatingΔμ when the updating cancellation condition does not apply) may use thephase compensation element 26 ea to determine the frictional coefficientincreasing/decreasing manipulated variable Δμ as described above.

Further, when carrying out the determination processing in S122-5-1,Mnsp_sens f and Mnsp_estm_f may be used in place of Mnsp_sens andMnsp_estm to carry out the determination processing.

Further, in the present embodiment, the μ sensitivity p has been passedthrough both the filter 26 db and the saturation characteristic element26 g. However, if the magnitude of the μ sensitivity p is not expectedto increase much, then the saturation characteristic element 26 g may beomitted.

Eighth Embodiment

An eighth embodiment of the present invention will now be described withreference to FIG. 21. The present embodiment differs from the aforesaidseventh embodiment only partly in the processing carried out by theaforesaid μ estimator 26.

To be more specific, a μ estimator 26 in the present embodiment furtherincludes a dead-zone processor 26 ha which receives an NSP yaw momentfiltering estimation error Mnsp_err f calculated by the aforesaidMnsp_err calculator 26 c and a dead-zone processor 26 hb which receivesa μ-sensitivity-dependent value p_fa obtained by passing a μ sensitivityp through the aforesaid filter 26 db and the saturation characteristicelement 26 g.

If an input value to the dead-zone processor 26 ha is in a predetermineddead zone in the vicinity of zero, which has been set beforehand, thenthe dead-zone processor 26 ha outputs zero. If the input value to thedead-zone processor 26 ha is larger than an upper limit value (>0) ofthe dead zone, then the dead-zone processor 26 ha outputs a valueobtained by subtracting the upper limit value from the input value. Ifthe input value to the dead-zone processor 26 ha is smaller than a lowerlimit value (=−upper limit value) of the dead zone, then the dead-zoneprocessor 26 ha outputs a value obtained by subtracting the lower limitvalue from the input value. The same applies to the dead-zone processor26 hb. The dead zones of the dead-zone processors 26 ha and 26 hb do nothave to be the same zones.

According to the present embodiment, the NSP yaw moment filteringestimation error Mnsp_err_fa, which is an output of the dead-zoneprocessor 26 ha having received Mnsp_err f, and theμ-sensitivity-dependent value p_fb, which is an output of the dead-zoneprocessor 26 hb having received p_fa, are input in place of Mnsp_err andμ to a frictional coefficient increasing/decreasing manipulated variabledeterminer 26 e. Further, according to the present embodiment, thefrictional coefficient increasing/decreasing manipulated variabledeterminer 26 e uses the supplied Mnsp_err_fa and p_fb to determine thefrictional coefficient increasing/decreasing manipulated variable Δμ bythe same processing as that in the seventh embodiment.

The present embodiment is the same as the aforesaid seventh embodimentexcept for the aspects described above.

In addition to providing the same advantages as those of the aforesaidseventh embodiment, the present embodiment makes it possible to removesteady unwanted components included in Mnsp_sens, Mnsp_estm, and pattributable to a steady offset or drift in an output of a sensor, suchas a yaw rate sensor 13 or a lateral acceleration sensor 15, or anactual road surface bank angle θbank_act by the dead-zone processors 26ha and 26 hb. As a result, the accuracy of μ_estm can be furtherenhanced.

Supplementally, determining the frictional coefficientincreasing/decreasing manipulated variable Δμ by using the dead-zoneprocessors 26 ha and 26 hb as in the present embodiment can be appliedalso to the first or the second embodiment described above.

In this case, the processing in S122-5-4 (the processing for calculatingΔμ when the updating cancellation condition does not apply) may use thephase compensation element 26 ea to determine the frictional coefficientincreasing/decreasing manipulated variable Δμ as with the aforesaidpresent embodiment.

Regarding the determination processing related to the updatingcancellation condition, the determination processing in S122-5-1 may useMnsp_sens_f and Mnsp_estm_f in place of Mnsp_sens and Mnsp_estm,respectively.

Further, in the present embodiment, the μ sensitivity p has been passedthrough both the filter 26 db and the saturation characteristic element26 g. However, in the case where the magnitude of the μ sensitivity p isnot expected to increase much, then the saturation characteristicelement 26 g may be omitted.

The present embodiment is provided with the dead-zone processor 26 ha towhich Mnsp_err_f is input and the dead-zone processor 26 hb to whichp_fa is input. Alternatively, however, one of the dead-zone processors26 ha and 26 hb may be omitted.

In the first to the eighth embodiments described above, thedriving/braking force estimated value Fsubx_i_estm of each wheel 2-i andthe lateral force estimated value Fsuby_i_estm have been determined andthe value of Mnsp_estm has been calculated on the basis of the estimatedvalues in order to determine the NSP yaw moment estimated valueMnsp_estm.

However, the actual NSP yaw moment Mnsp_act generally exhibits highdependency upon the lateral force out of the lateral force and thedriving/braking force of each wheel 2-i and low dependency upon thedriving/braking force. Hence, the step of determining thedriving/braking force estimated value Fsubx_i_estm of each wheel 2-i maybe omitted. In this case, for example, the lateral translational forceacting on the center-of-gravity point of a vehicle 1 due to theresultant force of the lateral force estimated values Fsuby_i_estm ofthe wheels 2-i(i=1, 2, 3, 4) and the moment about a yaw axis acting onthe center-of-gravity point of the vehicle 1 due to the resultant forceof the lateral force estimated values Fsuby_i_estm may be determined asthe total road surface reaction force resultant lateral force estimatedvalue Fgy_total_estm and the total road surface reaction force resultantyaw moment estimated value Mgz_total_estm, respectively. Then, based onthe determined Fgy_total_estm and Mgz_total_estm, the NSP yaw momentestimated value Mnsp_estm may be determined according to the aforesaidexpression 7-1.

The side slip motion of the vehicle 1 is also highly dependent upon thelateral force out of the lateral force and the driving/braking force ofeach wheel 2-i. Therefore, when estimating the side slip angle motionstate amount of the vehicle 1 by the vehicle motion estimator 24 d, onlythe lateral translational force acting on the center-of-gravity point ofthe vehicle 1 due to the resultant force of the lateral force estimatedvalues Fsuby_i_estm of the wheels 2-i(i=1, 2, 3, 4) may be regarded asthe entire lateral external force (translational force) acting on thecenter-of-gravity point of the vehicle 1 to estimate the side slipmotion state amount of the vehicle 1.

For example, the value of the lateral translational force acting on thecenter-of-gravity point of the vehicle 1 due to the resultant force ofthe lateral force estimated values Fsuby_i_estm of the wheels 2-i(i=1,2, 3, 4) is determined as the total road surface reaction forceresultant lateral force estimated values Fgy_total_estm. Then, thecalculation of the aforesaid expression 1-14a is performed by using theFgy_total_estm to determine a vehicle center of gravity side slipvelocity change rate estimated value Vgdot_y_estm. Then, the determinedVgdot_y_estm is integrated to determine the vehicle center of gravityside slip velocity estimated value Vgy_estm.

In the first to the eighth embodiments described above, the μsensitivity p has been calculated according to the aforesaid expression5-7 in the processing of S122-4 in FIG. 12. Alternatively, however, theμ sensitivity may be calculated by using the aforesaid frictioncharacteristic model.

For example, the same processing as that in S110 and 5112 of FIG. 4 iscarried out using the value of the road surface frictional coefficient,which is obtained by changing μ_estm_p by a predetermined minute amountdμ set beforehand (=μ_estm_p+dμ), in place of a latest value (a previousvalue) of the road surface frictional coefficient estimated valueμ_estm_p, thereby calculating the total road surface reaction forceresultant lateral force estimated values Fgy_total_estm (the lateralcomponent of the total road surface reaction force translational forcevector estimated value ↑Fg_total_estm) and the total road surfacereaction force yaw moment Mgz_total_estm in the case where it is assumedthat the value of the road surface frictional coefficient is 82_estm_p+dμ.

Then, the right side of the aforesaid expression 7-1 is calculated usingthe obtained Fgy_total_estm and Mgz_total_estm thereby to calculate theNSP yaw moment estimated value (hereinafter referred to as Mnsp_estm2)in the case where it is assumed that the value of the road surfacefrictional coefficient is μ_estm_p+dμ.

Subsequently, the difference between the calculated NSP yaw momentestimated value Mnsp_estm2 and the NSP yaw moment estimated valueMnsp_estm (the NSP yaw moment estimated value in the case where it isassumed that the value of the road surface frictional coefficient isμ_estm_p) calculated in the aforesaid S122-2 (=Mnsp_estm2−Mnsp_estm) isdivided by dμ to calculate the μ sensitivity p.

Further, in the first to the eighth embodiments described above, the NSPyaw moment has been used as the to-be-compared external force in thepresent invention. However, the to-be-compared external force in thepresent invention is not limited to the NSP yaw moment. For example, thelateral component of the vehicle 1 (a component in the direction of theY-axis of a vehicle body coordinate system) of the resultant force ofthe road surface reaction forces (more specifically, the driving/brakingforce and the lateral force) of the front wheels 2-1 and 2-2 may be usedas the to-be-compared external force.

Further, in the first to the eighth embodiments described above, thevalue of p calculated by the aforesaid expression 5-7 has been used asthe μ sensitivity. Alternatively, however, the value obtained bydividing the value of p by a latest value (a previous value) of the roadsurface frictional coefficient estimated value μ_estm (the ratio of prelative to the latest value of μ_estm) may be defined as the μsensitivity, and the defined μ sensitivity may be used in place of p todetermine the frictional coefficient increasing/decreasing manipulatedvariable Δμ.

Further, in the first to the eighth embodiments described above, thefrictional coefficient increasing/decreasing manipulated variable Δμ hasbeen determined by the processing in S122-5-4 only in the case where theupdating cancellation condition does not apply. Alternatively, however,the frictional coefficient increasing/decreasing manipulated variable Δμcan be determined without determining whether the updating cancellationcondition applies.

For example, the processing by the frictional coefficientincreasing/decreasing manipulated variable determiner 26 e omits theprocessing by the aforesaid gain adjustor. Further, the value of thegain adjustment parameter Kmu_att is always set to 1 or Kmu_att isdetermined by the processing in S122-5-6 to S122-5-10. In other words,Kmu_att is determined by the processing in S122-5-2 or the processing inS122-5-6 to S122-5-10 regardless of the determination result in theS122-5-1 or S122-5-20. Then, the frictional coefficientincreasing/decreasing manipulated variable Δμ may be determined by theprocessing in S122-5-4 by using the gain adjustment parameter Kmu_attdetermined as described above.

Further, each of the first to the eighth embodiments described above hasbeen provided with the bank angle estimator 28 and the slope angleestimator 30. However, the processing for estimating the road surfacefrictional coefficient μ in the first to the eighth embodiments does notneed the road surface bank angle estimated value θbank_estm and the roadsurface slope angle estimated value θslope_estm. Hence, the bank angleestimator 28 and the slope angle estimator 30 may be omitted.

The processing by the vehicle model calculator 24 has used the vehiclemotion model based on the assumption that a road surface is horizontal.Alternatively, however, a vehicle motion model taking the road surfacebank angle θbank and the road surface slope angle θslope into accountmay be used. For example, a vehicle motion model that has replaced theaforesaid expressions 1-13 and 1-14 by the following expressions 1-13band 1-14b, respectively, may be used.

Fgx_total=m*(Vgdot _(—) x−Vgy*γ−g*sin(θ slope))   Expression 1-13b

Fgy_total=m*(Vgdot _(—) y+Vgx*γ+g*sin(θ bank))   Expression 1-14b

In this case, for example, the vehicle model calculator 24 can estimatethe road surface bank angle θbank and the road surface slope angleθslope while determining the vehicle center of gravity longitudinalvelocity estimated value Vgx_estm and the vehicle center of gravity sideslip velocity estimated value Vgy_estm as described below.

To be specific, in this case, the vehicle model calculator 24 calculatesthe vehicle center of gravity longitudinal velocity change rateestimated value Vgdot_x_estm and the vehicle center of gravity side slipvelocity change rate estimated value Vgdot_y_estm according to thefollowing expressions 1-13c and 1-14c in place of the aforesaidexpressions 1-13a and 1-14a, respectively.

Vgdot _(—) x_estm=Fgx_total_estm/m+Vgy_estm₁₃ p*γ_estm_(—) p+g*sin(74slope_estm_(—) p)   Expression 1-13c

Vgdot _(—) y_estm=Fgy_total_estm/m−Vgx_estm_(—) p*γ_estm_(—) p−g*sin(θbank_estm_(—) p)   Expression 1-14c

Then, the vehicle model calculator 24 uses the Vgdot_x_estm andVgdot_y_estm to determine the vehicle center of gravity longitudinalvelocity estimated value Vg_estm and the vehicle center of gravity sideslip velocity estimated value Vgy_estm, as with the first embodimentdescribed above. The vehicle center of gravity longitudinal velocityestimated value Vgx_estm may be set to agree with the aforesaid selectedwheel speed detected value Vw_i_sens select.

Further, the vehicle model calculator 24 calculates the sensed-by-sensorlongitudinal acceleration estimated value Accx_sensor_estm, which is anestimated value of acceleration sensed by the longitudinal accelerationsensor 14, and the sensed-by-sensor lateral acceleration estimated valueAccy_sensor_estm, which is an estimated value of acceleration sensed bythe lateral acceleration sensor 15, according to expressions 1-31 and1-32 given below.

Accx_sensor_estm=Vgdot_x_estm−Vgy_estm_(—) p*γ_estm_(p−g)*sin(θslope_estm_(—) p)   Expression 1-31

Accy_sensor_estm=Vgdot _(—) y_estm+Vgx_estm_(—) p*γ_estmp+g* sin(θbank_estm_(—) p)   Expression 1-32

The values of Accx_sensor_estm and Accy_sensor_estm may be determined bycalculating the first term of the right side of expression 1-13c andcalculating the first term of the right side of expression 1-14c insteadof using expressions 1-31 and 1-32, respectively.

Here, Accx_sensor_estm determined as described above means asensed-by-sensor longitudinal acceleration estimated value determined onthe assumption that a previous value (a latest value) θslope_estm_p of aroad surface slope angle estimated value is accurate. Similarly,Accy_sensor_estm determined as described above means a sensed-by-sensorlateral acceleration estimated value determined on the assumption that aprevious value (a latest value) θbank_estm_p of a road surface bankangle estimated value is accurate.

Accordingly, the difference between the vehicle center of gravitylongitudinal acceleration detected value Accx_sens (=sensed-by-sensorlongitudinal acceleration detected value) based on an output of thelongitudinal acceleration sensor 14 and the sensed-by-sensorlongitudinal acceleration estimated value Accx_sensor_estm is consideredto be based on an error of θslope_estm_p.

Similarly, the difference between the vehicle center of gravity lateralacceleration detected value Accy_sens (=sensed-by-sensor lateralacceleration detected value) based on an output of the lateralacceleration sensor 15 and the sensed-by-sensor lateral accelerationestimated value Accy_sensor_estm is considered to be based on an errorof θbank_estm_p.

Thus, the vehicle model calculator 24 determines a new road surfaceslope angle estimated value θslope_estm by updating the road surfaceslope angle estimated value θslope_estm according to a feedback controllaw on the basis of the difference between the vehicle center of gravitylongitudinal acceleration detected value Accx_sens and thesensed-by-sensor longitudinal acceleration estimated valueAccx_sensor_estm such that the difference is converged to zero.Similarly, the vehicle model calculator 24 determines a new road surfacebank angle estimated value θbank_estm by updating the value θbank_estmaccording to the feedback control law on the basis of the differencebetween the vehicle center of gravity lateral acceleration detectedvalue Accy_sens and the sensed-by-sensor lateral acceleration estimatedvalue Accy_sensor estm such that the difference is converged to zero.

For example, the vehicle model calculator 24 determines the new roadsurface slope angle estimated value θslope_estm and the road surfacebank angle estimated value θbank angle_estm, respectively, according toexpressions 1-33 and 1-34 given below.

θ slope_estm=θ slope_estm_(—) p+Kslope*(Accx _(—) sens−Accx_sensor_estm)  Expression 1-33

θ bank_estm=θ bank_estm_(—) p+Kbank*(Accy _(—) sens−Accy_sensor_estm)  Expression 1-34

Kslope in expression 1-33 and Kbank in expression 1-34 denotepredetermined values (proportional gains) set beforehand. In thisexample, the integral calculation of the difference(Accx_sens−Accx_sensor_estm) and the difference(Accy_sens−Accy_sensor_estm) is performed to calculate θslope_estm andθbank_estm.

Thus, the road surface bank angle θbank and the road surface slope angleθslope can be estimated while determining the vehicle center of gravitylongitudinal velocity estimated value Vgx_estm and the vehicle center ofgravity side slip velocity estimated value Vgy_estm.

In this case, there is no need to calculate the vehicle center ofgravity longitudinal acceleration estimated value Accx_estm or thevehicle center of gravity lateral acceleration estimated valueAccy_estm. Further, in this case, the relationship represented by theaforesaid expression 1-14b corresponds to the dynamic relationshiprelated to the vehicle motion/road surface reaction force estimator.

1. A road surface frictional coefficient estimating apparatus whichestimates a frictional coefficient of a road surface on which a vehicleis traveling while updating the frictional coefficient, comprising:first estimating means of a to-be-compared external force which definesa predetermined type of an external force component acting on a vehicledue to the resultant force of road surface reaction forces acting oneach wheel of the vehicle from a road surface as a to-be-comparedexternal force and determines a first estimated value of theto-be-compared external force by using a friction characteristic modelindicating a relationship between a slip between a wheel of the vehicleand the road surface and a road surface reaction force, an estimatedvalue of a frictional coefficient already determined, and an observedvalue of a predetermined type of an amount to be observed, which isrelated to a behavior of the vehicle; second estimating means of ato-be-compared external force which determines a value of an externalforce component balancing out an inertial force corresponding to theto-be-compared external force on the basis of an observed value of amotional state amount of the vehicle that defines the inertial force,which is a part of an inertial force generated by a motion of thevehicle, and obtains the determined value of the external forcecomponent as a second estimated value of the to-be-compared externalforce; frictional coefficient increasing/decreasing manipulated variabledetermining means which determines an increasing/decreasing manipulatedvariable of an estimated value of the frictional coefficient of the roadsurface on the basis of at least the first estimated value and thesecond estimated value; and frictional coefficient estimated valueupdating means which determines a new estimated value of a frictionalcoefficient by updating the estimated value of the frictionalcoefficient of the road surface on the basis of theincreasing/decreasing manipulated variable, wherein the frictionalcoefficient increasing/decreasing manipulated variable determining meanscomprises updating cancellation condition determining means whichdetermines whether or not a predetermined updating cancellationcondition applies, the condition including at least a condition that thefirst estimated value and the second estimated value have polaritiesopposite to each other, and determines the increasing/decreasingmanipulated variable on the basis of at least a difference between thefirst estimated value and the second estimated value such that thedifference therebetween is converged to zero provided that at least adetermination result of the updating cancellation condition determiningmeans is negative, and determines either zero or a manipulated variableof a predetermined value for incrementing the estimated value of thefrictional coefficient as the increasing/decreasing manipulated variablein the case where the determination result is affirmative.
 2. The roadsurface frictional coefficient estimating apparatus according to claim1, wherein in the case where the determination result given by theupdating cancellation condition determining means has changed fromaffirmative over to negative, the frictional coefficientincreasing/decreasing manipulated variable determining means determinesthe increasing/decreasing manipulated variable on the basis of at leastthe difference, provided that a status wherein the determination resultremains negative lasts for predetermined time or more after thechangeover, and determines, as the increasing/decreasing manipulatedvariable, either zero or a manipulated variable of a predetermined valuefor incrementing the estimated value of the frictional coefficient untila status in which the determination result is negative lasts for thepredetermined time.
 3. The road surface frictional coefficientestimating apparatus according to claim 1, wherein the updatingcancellation condition further includes a condition that at least one ofthe first estimated value and the second estimated value falls within apredetermined range that has been preset as a range in the vicinity ofzero.
 4. The road surface frictional coefficient estimating apparatusaccording to claim 1, comprising: a μ sensitivity calculating meanswhich determines a value of a μ sensitivity which indicates a ratio ofthe incremental amount of the to-be-compared external force relative toan incremental amount of the frictional coefficient of the road surface,or a value of a μ sensitivity obtained by dividing the ratio by a valueof the frictional coefficient of the road surface, wherein the updatingcancellation condition further includes a condition that the value ofthe μ sensitivity has a polarity that is opposite to that of at leastone of the first estimated value and the second estimated value.
 5. Theroad surface frictional coefficient estimating apparatus according toclaim 4, wherein the updating cancellation condition further includes acondition that the value of the μ sensitivity is a value falling withina predetermined range that has been preset as a range in the vicinity ofzero.
 6. The road surface frictional coefficient estimating apparatusaccording to claim 4, wherein in the case of determining theincreasing/decreasing manipulated variable on the basis of thedifference, the frictional coefficient increasing/decreasing manipulatedvariable determining means determines the increasing/decreasingmanipulated variable on the basis of the difference and the value of theμ sensitivity.
 7. The road surface frictional coefficient estimatingapparatus according to claim 6, wherein in the case of determining theincreasing/decreasing manipulated variable on the basis of thedifference, the frictional coefficient increasing/decreasing manipulatedvariable determining means determines the increasing/decreasingmanipulated variable on the basis of the product of the difference andthe μ sensitivity, which is the product of the value of the differenceand the value of the μ sensitivity or the product of the difference andthe μ sensitivity, which is the product of the difference and aμ-sensitivity-dependent value, which is obtained by passing the value ofthe μ sensitivity through one or both of a third filter for regulatingfrequency components and a saturation characteristic element.
 8. Theroad surface frictional coefficient estimating apparatus according toclaim 7, wherein the frictional coefficient increasing/decreasingmanipulated variable determining means determines theincreasing/decreasing manipulated variable on the basis of the productof the difference and the μ sensitivity such that theincreasing/decreasing manipulated variable is proportional to theproduct of the difference and the μ sensitivity.
 9. The road surfacefrictional coefficient estimating apparatus according to claim 1,wherein the to-be-compared external force is a moment about a yaw axisat a neutral steer point of the vehicle.
 10. The road surface frictionalcoefficient estimating apparatus according to claim 4, wherein theto-be-compared external force is a moment about a yaw axis at a neutralsteer point of the vehicle, and the μ sensitivity calculating meansdetermines the value of the μ sensitivity by linearly coupling anobserved value of a steering angle of a steering control wheel amongwheels of the vehicle and an observed value of the yaw rate of thevehicle.
 11. The road surface frictional coefficient estimatingapparatus according to claim 10, wherein the μ sensitivity calculatingmeans sets at least one of a weighting factor applied to the observedvalue of the steering angle and a weighting factor applied to theobserved value of the yaw rate in the linear coupling on the basis of anobserved value of a vehicle speed of the vehicle such that the mutualratio of both weighting factors changes according to the vehicle speed,and uses the set weighting factor to carry out the calculation of thelinear coupling.
 12. The road surface frictional coefficient estimatingapparatus according to claim 9, wherein the first estimating means ofthe to-be-compared external force comprises a vehicle motion/roadsurface reaction force estimating means which estimates at least alateral force of the road surface reaction force acting on each wheelwhile estimating at least a side slip motional state amount of themotional state amount of the vehicle generated by the resultant force ofthe road surface reaction forces acting on each wheel of the vehicle,and determines a first estimated value of a moment about a yaw axis atthe neutral steer point by using the estimated value of the lateralforce that has been determined by the vehicle motion/road surfacereaction force estimating means, and the vehicle motion/road surfacereaction force estimating means comprises: means which determines anestimated value of a side slip angle as a slip of each wheel of thevehicle by using the observed value of the amount to be observed and theestimated value of the side slip motional state amount of the vehiclethat has already been determined; means which inputs at least theestimated value of the side slip angle of each wheel and the estimatedvalue of the frictional coefficient of the road surface that has alreadybeen determined to the friction characteristic model so as to determinethe estimated value of the lateral force acting on each wheel by thefriction characteristic model; and means which determines a newestimated value of the side slip motional state amount of the vehicle byusing a dynamic relationship between a resultant force of road surfacereaction forces including at least the lateral force acting on eachwheel and the side slip motional state amount of the vehicle and theestimated value of the lateral force acting on each wheel.
 13. The roadsurface frictional coefficient estimating apparatus according to claim9, wherein the first estimating means of the to-be-compared externalforce comprises a vehicle motion/road surface reaction force estimatingmeans which estimates a driving/braking force and a lateral force of aroad surface reaction force acting on each wheel while estimating atleast the side slip motional state amount of the motional state amountsof the vehicle generated by a resultant force of the road surfacereaction forces acting on each wheel of the vehicle, and determines afirst estimated value of a moment about the yaw axis at the neutralsteer point by using the estimated value of the lateral force determinedby the vehicle motion/road surface reaction force estimating means, andthe vehicle motion/road surface reaction force estimating meanscomprises: means which determines the estimated values of a slip rateand a side slip angle as a slip of each wheel of the vehicle by usingthe observed value of the amount to be observed and the estimated valueof the side slip motional state amount of the vehicle that has alreadybeen determined; means which inputs at least the estimated values of theslip rate and the side slip angle of each wheel and the estimated valueof the frictional coefficient of the road surface that has already beendetermined to the friction characteristic model so as to determine theestimated values of the driving/braking force and the lateral forceacting on each wheel by the friction characteristic model; and meanswhich determines a new estimated value of the side slip motional stateamount of the vehicle by using a dynamic relationship between theresultant force of road surface reaction forces including at least thedriving/braking force and the lateral force acting on each wheel and theside slip motional state amount of the vehicle and the estimated valueof the lateral force acting on each wheel.
 14. A road surface frictionalcoefficient estimating apparatus which estimates a frictionalcoefficient of a road surface on which a vehicle is traveling whileupdating the frictional coefficient, comprising: first estimating meansof a to-be-compared external force which defines a predetermined type ofan external force component acting on a vehicle due to a resultant forceof road surface reaction forces acting on each wheel of the vehicle froma road surface as a to-be-compared external force and which determines afirst estimated value of the to-be-compared external force by using afriction characteristic model indicating a relationship between a slipbetween a wheel of the vehicle and the road surface and a road surfacereaction force, an estimated value of a frictional coefficient alreadydetermined, and an observed value of a predetermined type of an amountto be observed, which is related to a behavior of the vehicle; secondestimating means of a to-be-compared external force which determines avalue of an external force component balancing out an inertial forcecorresponding to the to-be-compared external force on the basis of anobserved value of a motional state amount of the vehicle that definesthe inertial force, which is a part of an inertial force generated by amotion of the vehicle, and obtains the determined value of the externalforce component as a second estimated value of the to-be-comparedexternal force; frictional coefficient increasing/decreasing manipulatedvariable determining means which determines an increasing/decreasingmanipulated variable of an estimated value of the frictional coefficientof the road surface on the basis of at least the first estimated valueand the second estimated value; and frictional coefficient estimatedvalue updating means which determines a new estimated value of thefrictional coefficient by updating the estimated value of the frictionalcoefficient of a road surface on the basis of the increasing/decreasingmanipulated variable, wherein the frictional coefficientincreasing/decreasing manipulated variable determining means hasupdating cancellation condition determining means which determineswhether or not a predetermined updating cancellation condition applies,the condition including at least a condition that a first estimatedfiltering value obtained by passing the first estimated value through afirst filter for regulating frequency components and a second estimatedfiltering value obtained by passing the second estimated value through asecond filter for regulating frequency components carry polarities thatare opposite to each other, determines the increasing/decreasingmanipulated variable on the basis of at least a difference between thefirst estimated filtering value and the second estimated filtering valuesuch that the difference is converged to zero, provided that adetermination result of at least the updating cancellation conditiondetermining means is negative, and determines either zero or amanipulated variable of a predetermined value for increasing theestimated value of the frictional coefficient as theincreasing/decreasing manipulated variable in the case where thedetermination result is affirmative.
 15. The road surface frictionalcoefficient estimating apparatus according to claim 14, wherein in thecase where the determination result given by the updating cancellationcondition determining means has changed from affirmative over tonegative, the frictional coefficient increasing/decreasing manipulatedvariable determining means determines the increasing/decreasingmanipulated variable on the basis of at least the difference, providedthat a status wherein the determination result remains negative lastsfor predetermined time or more after the changeover, and determines, asthe increasing/decreasing manipulated variable, either zero or amanipulated variable of a predetermined value for incrementing theestimated value of the frictional coefficient until a status in whichthe determination result is negative lasts for the predetermined time.16. The road surface frictional coefficient estimating apparatusaccording to claim 14, wherein the updating cancellation conditionfurther includes a condition that at least one of the first estimatedfiltering value and the second estimated filtering value falls within apredetermined range that has been preset as a range in the vicinity ofzero.
 17. The road surface frictional coefficient estimating apparatusaccording to claim 14, comprising: μ sensitivity calculating means whichdetermines the value of a μ sensitivity, which indicates the ratio of anincremental amount of the to-be-compared external force relative to anincremental amount of the frictional coefficient of a road surface, orthe value of a μ sensitivity obtained by dividing the ratio by the valueof the frictional coefficient of the road surface, wherein the updatingcancellation condition further includes a condition that a μ sensitivityfiltering value obtained by passing the value of the μ sensitivitythrough a third filter for regulating frequency components has apolarity that is opposite to that of at least one of the first estimatedfiltering value and the second estimated filtering value.
 18. The roadsurface frictional coefficient estimating apparatus according to claim17, wherein the updating cancellation condition further includes acondition that the μ sensitivity filtering value is a value within apredetermined range that has been preset as a range in the vicinity ofzero.
 19. The road surface frictional coefficient estimating apparatusaccording to claim 17, wherein in the case of determining theincreasing/decreasing manipulated variable on the basis of thedifference, the frictional coefficient increasing/decreasing manipulatedvariable determining means determines the increasing/decreasingmanipulated variable on the basis of the difference and the μsensitivity filtering value.
 20. The road surface frictional coefficientestimating apparatus according to claim 19, wherein in the case ofdetermining the increasing/decreasing manipulated variable on the basisof the difference, the frictional coefficient increasing/decreasingmanipulated variable determining means determines theincreasing/decreasing manipulated variable on the basis of the productof the difference and the μ sensitivity, which is the product of thevalue of the difference and the value of the μ sensitivity filteringvalue or the product of the difference and a μ sensitivity, which is theproduct of the difference and a μ-sensitivity-dependent value, which isobtained by passing the μ sensitivity filtering value through asaturation characteristic element.
 21. The road surface frictionalcoefficient estimating apparatus according to claim 20, wherein thefrictional coefficient frictional coefficient increasing/decreasingmanipulated variable determining means determines theincreasing/decreasing manipulated variable, on the basis of the productof the difference and the μ sensitivity such that theincreasing/decreasing manipulated variable is proportional to theproduct of the difference and the μ sensitivity.
 22. The road surfacefrictional coefficient estimating apparatus according to claim 14,wherein the to-be-compared external force is a moment about a yaw axisat a neutral steer point of a vehicle.
 23. The road surface frictionalcoefficient estimating apparatus according to claim 17, wherein theto-be-compared external force is a moment about a yaw axis at a neutralsteer point of a vehicle, and the μ sensitivity calculating meansdetermines the value of the μ sensitivity by linearly coupling anobserved value of a steering angle of a steering control wheel among thewheels of the vehicle and an observed value of the yaw rate of thevehicle.
 24. The road surface frictional coefficient estimatingapparatus according to claim 23, wherein the μ sensitivity calculatingmeans sets at least one of a weighting factor applied to the observedvalue of the steering angle and a weighting factor applied to theobserved value of the yaw rate in the linear coupling on the basis ofthe observed value of a vehicle speed such that a mutual ratio of bothweighting factors changes according to the vehicle speed of the vehicle,and uses the set weighting factor to carry out the calculation of thelinear coupling.
 25. The road surface frictional coefficient estimatingapparatus according to claim 22, wherein the first estimating means ofthe to-be-compared external force comprises a vehicle motion/roadsurface reaction force estimating means which estimates at least alateral force of a road surface reaction force acting on each wheelwhile estimating at least a side slip motional state amount of amotional state amount of the vehicle generated by the resultant force ofthe road surface reaction forces acting on each wheel of the vehicle,and determines the first estimated value of a moment about the yaw axisat the neutral steer point by using the estimated value of the lateralforce that has been determined by the vehicle motion/road surfacereaction force estimating means, and the vehicle motion/road surfacereaction force estimating means comprises: means which determines theestimated value of a side slip angle as a slip of each wheel of thevehicle by using the observed value of the amount to be observed and theestimated value of the side slip motional state amount of the vehiclethat has already been determined; means which inputs at least theestimated value of the side slip angle of each wheel and the estimatedvalue of the frictional coefficient of the road surface that has alreadybeen determined to the friction characteristic model so as to determinethe estimated value of the lateral force acting on each wheel by thefriction characteristic model; and means which determines a newestimated value of the side slip motional state amount of the vehicle byusing a dynamic relationship between the resultant force of road surfacereaction forces including at least the lateral force acting on eachwheel and the side slip motional state amount of the vehicle and theestimated value of the lateral force acting on each wheel.
 26. The roadsurface frictional coefficient estimating apparatus according to claim22, wherein the first estimating means of the to-be-compared externalforce comprises a vehicle motion/road surface reaction force estimatingmeans which estimates the driving/braking force and the lateral force ofthe road surface reaction force acting on each wheel while estimating atleast the side slip motional state amount of the motional state amountof the vehicle generated by the resultant force of the road surfacereaction forces acting on each wheel of the vehicle, and determines thefirst estimated value of a moment about the yaw axis at the neutralsteer point by using the estimated value of the lateral force that hasbeen determined by the vehicle motion/road surface reaction forceestimating means, and the vehicle motion/road surface reaction forceestimating means comprises: means which determines the estimated valuesof a slip rate and a side slip angle as a slip of each wheel of thevehicle by using the observed value of the amount to be observed and theestimated value of the side slip motional state amount of the vehiclethat has already been determined; means which inputs at least theestimated values of the slip rate and the side slip angle of each wheeland the estimated value of the frictional coefficient of the roadsurface that has already been determined to the friction characteristicmodel so as to determine the estimated values of the driving/brakingforce and the lateral force acting on each wheel by the frictioncharacteristic model; and means which determines a new estimated valueof the side slip motional state amount of the vehicle by using a dynamicrelationship between the resultant force of road surface reaction forcesincluding at least the driving/braking force and the lateral forceacting on each wheel and the side slip motional state amount of thevehicle and the estimated value of the lateral force acting on eachwheel.
 27. A road surface frictional coefficient estimating apparatuswhich estimates a frictional coefficient of a road surface on which avehicle is traveling while updating the frictional coefficient,comprising: first estimating means of a to-be-compared external forcewhich defines a predetermined type of an external force component actingon a vehicle due to a resultant force of road surface reaction forcesacting on each wheel of the vehicle from a road surface as ato-be-compared external force and determines a first estimated value ofthe to-be-compared external force by using a friction characteristicmodel indicating a relationship between a slip between a wheel of thevehicle and the road surface and a road surface reaction force, anestimated value of a frictional coefficient already determined, and anobserved value of a predetermined type of an amount to be observed,which is related to a behavior of the vehicle; second estimating meansof a to-be-compared external force which determines a value of anexternal force component balancing out an inertial force correspondingto the to-be-compared external force on the basis of an observed valueof a motional state amount of the vehicle that defines the inertialforce, which is a part of an inertial force generated by a motion of thevehicle, and obtains the determined value of the external forcecomponent as a second estimated value of the to-be-compared externalforce; μ sensitivity calculating means which determines the value of a μsensitivity which indicates the ratio of an incremental amount of theto-be-compared external force relative to an incremental amount of thefrictional coefficient of a road surface, or the value obtained bydividing the ratio by the value of the frictional coefficient of theroad surface; frictional coefficient increasing/decreasing manipulatedvariable determining means which determines an increasing/decreasingmanipulated variable of an estimated value of the frictional coefficientof the road surface on the basis of at least a difference between thefirst estimated value and the second estimated value or a differencebetween a first estimation filtering value obtained by passing the firstestimated value through a first filter for regulating frequencycomponents and a second estimation filtering value obtained by passingthe second estimated value through a second filter for regulatingfrequency components, and a μ sensitivity value or aμ-sensitivity-dependent value obtained by passing the μ sensitivityvalue through one or both of a third filter for regulating frequencycomponents and a saturation characteristic element such that thedifference is converged to zero; and frictional coefficient estimatedvalue updating means which determines a new estimated value of africtional coefficient by updating the estimated value of the frictionalcoefficient of a road surface on the basis of the increasing/decreasingmanipulated variable, wherein the frictional coefficientincreasing/decreasing manipulated variable determining means determinesthe increasing/decreasing manipulated variable such that the magnitudeof the increasing/decreasing manipulated variable decreases as themagnitude of the μ sensitivity value or the μ-sensitivity-dependentvalue decreases.